rklib_variable_steps

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkbs32 module subroutine rkbs32(me, t, x, h, xf, xerr)

Bogacki-Shampine 3(2) method

Arguments

Type	Intent	Attributes		Name
class(rkbs32_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkssp43 module subroutine rkssp43(me, t, x, h, xf, xerr)

4-stage, 3rd order SSP Runge-Kutta method.

Arguments

Type	Intent	Attributes		Name
class(rkssp43_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf45 module subroutine rkf45(me, t, x, h, xf, xerr)

Fehlberg's 4(5) method.

Arguments

Type	Intent	Attributes		Name
class(rkf45_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkck54 module subroutine rkck54(me, t, x, h, xf, xerr)

Runge Kutta Cash-Karp.

Arguments

Type	Intent	Attributes		Name
class(rkck54_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkdp54 module subroutine rkdp54(me, t, x, h, xf, xerr)

Dormand-Prince 5(4) method (RKDP or DOPRI)

Arguments

Type	Intent	Attributes		Name
class(rkdp54_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkt54 module subroutine rkt54(me, t, x, h, xf, xerr)

Tsitouras 5(4) method

Arguments

Type	Intent	Attributes		Name
class(rkt54_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rks54 module subroutine rks54(me, t, x, h, xf, xerr)

Stepanov 5(4) method.

Arguments

Type	Intent	Attributes		Name
class(rks54_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkpp54 module subroutine rkpp54(me, t, x, h, xf, xerr)

Papakostas-PapaGeorgiou 5(4) method (more stable, higher error)

Arguments

Type	Intent	Attributes		Name
class(rkpp54_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkpp54b module subroutine rkpp54b(me, t, x, h, xf, xerr)

Papakostas-PapaGeorgiou 5(4) method (less stable, lower error).

Arguments

Type	Intent	Attributes		Name
class(rkpp54b_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkbs54 module subroutine rkbs54(me, t, x, h, xf, xerr)

Bogacki & Shampine 5(4)

Arguments

Type	Intent	Attributes		Name
class(rkbs54_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkss54 module subroutine rkss54(me, t, x, h, xf, xerr)

Sharp & Smart 5(4) method.

Arguments

Type	Intent	Attributes		Name
class(rkss54_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkdp65 module subroutine rkdp65(me, t, x, h, xf, xerr)

Dormand-Prince 6(5) method. This is RK6(5)8M from the reference.

Arguments

Type	Intent	Attributes		Name
class(rkdp65_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkc65 module subroutine rkc65(me, t, x, h, xf, xerr)

Calvo 6(5) method.

Arguments

Type	Intent	Attributes		Name
class(rkc65_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv65e module subroutine rkv65e(me, t, x, h, xf, xerr)

Verner's "most efficient" Runge-Kutta (9,6(5)) pair.

Arguments

Type	Intent	Attributes		Name
class(rkv65e_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktf65 module subroutine rktf65(me, t, x, h, xf, xerr)

Tsitouras & Famelis Runge-Kutta 6(5) method.

Arguments

Type	Intent	Attributes		Name
class(rktf65_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv65r module subroutine rkv65r(me, t, x, h, xf, xerr)

Verner's "most robust" Runge-Kutta (9,6(5)) pair.

Arguments

Type	Intent	Attributes		Name
class(rkv65r_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv65 module subroutine rkv65(me, t, x, h, xf, xerr)

Verner 6(5) method.

Arguments

Type	Intent	Attributes		Name
class(rkv65_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html dverk65 module subroutine dverk65(me, t, x, h, xf, xerr)

Verner 6(5) 'DVERK' method.

Arguments

Type	Intent	Attributes		Name
class(dverk65_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv76e module subroutine rkv76e(me, t, x, h, xf, xerr)

Verner's "most efficient" Runge-Kutta (10:7(6)) pair.

Arguments

Type	Intent	Attributes		Name
class(rkv76e_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv76r module subroutine rkv76r(me, t, x, h, xf, xerr)

Verner's "most robust" Runge-Kutta (10:7(6)) pair.

Arguments

Type	Intent	Attributes		Name
class(rkv76r_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkss76 module subroutine rkss76(me, t, x, h, xf, xerr)

Sharp & Smart 7(6)) method.

Arguments

Type	Intent	Attributes		Name
class(rkss76_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv87e module subroutine rkv87e(me, t, x, h, xf, xerr)

Verner's "most efficient" Runge-Kutta (13:8(7)) pair.

Arguments

Type	Intent	Attributes		Name
class(rkv87e_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv87r module subroutine rkv87r(me, t, x, h, xf, xerr)

Verner's "most robust" Runge-Kutta (13:8(7)) pair.

Arguments

Type	Intent	Attributes		Name
class(rkv87r_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkk87 module subroutine rkk87(me, t, x, h, xf, xerr)

Kovalnogov, Fedorov, Karpukhina, Simos, Tsitouras 8(7) method

Arguments

Type	Intent	Attributes		Name
class(rkk87_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv98e module subroutine rkv98e(me, t, x, h, xf, xerr)

Verner's "most efficient" Runge-Kutta (16:9(8)) pair.

Arguments

Type	Intent	Attributes		Name
class(rkv98e_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv98r module subroutine rkv98r(me, t, x, h, xf, xerr)

Verner's "most robust" Runge-Kutta (16:9(8)) pair.

Arguments

Type	Intent	Attributes		Name
class(rkv98r_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktp64 module subroutine rktp64(me, t, x, h, xf, xerr)

Tsitouras & Papakostas NEW6(4) Runge-Kutta method.

Arguments

Type	Intent	Attributes		Name
class(rktp64_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf78 module subroutine rkf78(me, t, x, h, xf, xerr)

Fehlberg's 7(8) algorithm.

Arguments

Type	Intent	Attributes		Name
class(rkf78_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkdp87 module subroutine rkdp87(me, t, x, h, xf, xerr)

Dormand-Prince RK8(7)13M method.

Arguments

Type	Intent	Attributes		Name
class(rkdp87_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv78 module subroutine rkv78(me, t, x, h, xf, xerr)

Verner's 7(8) algorithm.

Arguments

Type	Intent	Attributes		Name
class(rkv78_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html dverk78 module subroutine dverk78(me, t, x, h, xf, xerr)

Verner's "Maple" (dverk78).

Arguments

Type	Intent	Attributes		Name
class(dverk78_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktp75 module subroutine rktp75(me, t, x, h, xf, xerr)

Tsitouras & Papakostas NEW7(5) Runge-Kutta method.

Arguments

Type	Intent	Attributes		Name
class(rktp75_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktmy7 module subroutine rktmy7(me, t, x, h, xf, xerr)

Tanaka/Muramatsu/Yamashita 7th order (a.k.a. Tanyam7)

Arguments

Type	Intent	Attributes		Name
class(rktmy7_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktmy7s module subroutine rktmy7s(me, t, x, h, xf, xerr)

Tanaka/Muramatsu/Yamashita 7th order (stable alternate)

Arguments

Type	Intent	Attributes		Name
class(rktmy7s_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkdp85 module subroutine rkdp85(me, t, x, h, xf, xerr)

Dormand-Prince 8(5)

Arguments

Type	Intent	Attributes		Name
class(rkdp85_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktp86 module subroutine rktp86(me, t, x, h, xf, xerr)

Tsitouras & Papakostas NEW8(6): 12-stage, 8th and 6th order Runge-Kutta method.

Arguments

Type	Intent	Attributes		Name
class(rktp86_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkev87 module subroutine rkev87(me, t, x, h, xf, xerr)

Enright Verner 8(7)

Arguments

Type	Intent	Attributes		Name
class(rkev87_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf89 module subroutine rkf89(me, t, x, h, xf, xerr)

Fehlberg 8(9) method.

Arguments

Type	Intent	Attributes		Name
class(rkf89_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv89 module subroutine rkv89(me, t, x, h, xf, xerr)

Runge Kutta Verner 8(9)

Arguments

Type	Intent	Attributes		Name
class(rkv89_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkt98a module subroutine rkt98a(me, t, x, h, xf, xerr)

Tsitouras combined order 9(8) Runge-Kutta scheme A.

Arguments

Type	Intent	Attributes		Name
class(rkt98a_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rks98 module subroutine rks98(me, t, x, h, xf, xerr)

Sharp 9(8)

Arguments

Type	Intent	Attributes		Name
class(rks98_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf108 module subroutine rkf108(me, t, x, h, xf, xerr)

Feagin's RK8(10) method -- a 10th-order method with an embedded 8th-order method.

Arguments

Type	Intent	Attributes		Name
class(rkf108_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkc108 module subroutine rkc108(me, t, x, h, xf, xerr)

A modification of Curtis' order 10 Runge-Kutta scheme with an order 8 embedded scheme

Arguments

Type	Intent	Attributes		Name
class(rkc108_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkb109 module subroutine rkb109(me, t, x, h, xf, xerr)

Baker 10(9) method.

Arguments

Type	Intent	Attributes		Name
class(rkb109_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf1210 module subroutine rkf1210(me, t, x, h, xf, xerr)

Feagin's RK12(10) method -- a 12th-order method with an embedded 10th-order method.

Arguments

Type	Intent	Attributes		Name
class(rkf1210_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf1412 module subroutine rkf1412(me, t, x, h, xf, xerr)

Feagin's RK14(12) - a 14th-order method with an embedded 12th-order method.

Arguments

Type	Intent	Attributes		Name
class(rkf1412_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rko129 module subroutine rko129(me, t, x, h, xf, xerr)

A modification of Hiroshi Ono's order 12 Runge-Kutta scheme with an order 9 embedded scheme.

Arguments

Type	Intent	Attributes		Name
class(rko129_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rks1110a module subroutine rks1110a(me, t, x, h, xf, xerr)

Stone's 26 stage combined order 10 and 11 Runge-Kutta scheme

Arguments

Type	Intent	Attributes		Name
class(rks1110a_class),	intent(inout)		::	me
real(kind=wp),	intent(in)		::	t	initial time
real(kind=wp),	intent(in),	dimension(me%n)	::	x	initial state
real(kind=wp),	intent(in)		::	h	time step
real(kind=wp),	intent(out),	dimension(me%n)	::	xf	state at time `t+h`
real(kind=wp),	intent(out),	dimension(me%n)	::	xerr	truncation error estimate for `x`

rklib_variable_steps Submodule

Contents

Module Procedures

Uses

Ancestors:

Module Procedures

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkbs32 module subroutine rkbs32(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkssp43 module subroutine rkssp43(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf45 module subroutine rkf45(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkck54 module subroutine rkck54(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkdp54 module subroutine rkdp54(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkt54 module subroutine rkt54(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rks54 module subroutine rks54(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkpp54 module subroutine rkpp54(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkpp54b module subroutine rkpp54b(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkbs54 module subroutine rkbs54(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkss54 module subroutine rkss54(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkdp65 module subroutine rkdp65(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkc65 module subroutine rkc65(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv65e module subroutine rkv65e(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktf65 module subroutine rktf65(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv65r module subroutine rkv65r(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv65 module subroutine rkv65(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html dverk65 module subroutine dverk65(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv76e module subroutine rkv76e(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv76r module subroutine rkv76r(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkss76 module subroutine rkss76(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv87e module subroutine rkv87e(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv87r module subroutine rkv87r(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkk87 module subroutine rkk87(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv98e module subroutine rkv98e(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv98r module subroutine rkv98r(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktp64 module subroutine rktp64(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf78 module subroutine rkf78(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkdp87 module subroutine rkdp87(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv78 module subroutine rkv78(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html dverk78 module subroutine dverk78(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktp75 module subroutine rktp75(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktmy7 module subroutine rktmy7(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktmy7s module subroutine rktmy7s(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkdp85 module subroutine rkdp85(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktp86 module subroutine rktp86(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkev87 module subroutine rkev87(me, t, x, h, xf, xerr) Interface →

Arguments

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkbs32 module subroutine rkbs32(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkssp43 module subroutine rkssp43(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf45 module subroutine rkf45(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkck54 module subroutine rkck54(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkdp54 module subroutine rkdp54(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkt54 module subroutine rkt54(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rks54 module subroutine rks54(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkpp54 module subroutine rkpp54(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkpp54b module subroutine rkpp54b(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkbs54 module subroutine rkbs54(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkss54 module subroutine rkss54(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkdp65 module subroutine rkdp65(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkc65 module subroutine rkc65(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv65e module subroutine rkv65e(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktf65 module subroutine rktf65(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv65r module subroutine rkv65r(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv65 module subroutine rkv65(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html dverk65 module subroutine dverk65(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv76e module subroutine rkv76e(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv76r module subroutine rkv76r(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkss76 module subroutine rkss76(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv87e module subroutine rkv87e(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv87r module subroutine rkv87r(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkk87 module subroutine rkk87(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv98e module subroutine rkv98e(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv98r module subroutine rkv98r(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktp64 module subroutine rktp64(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf78 module subroutine rkf78(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkdp87 module subroutine rkdp87(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv78 module subroutine rkv78(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html dverk78 module subroutine dverk78(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktp75 module subroutine rktp75(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktmy7 module subroutine rktmy7(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktmy7s module subroutine rktmy7s(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkdp85 module subroutine rkdp85(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rktp86 module subroutine rktp86(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkev87 module subroutine rkev87(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf89 module subroutine rkf89(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkv89 module subroutine rkv89(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkt98a module subroutine rkt98a(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rks98 module subroutine rks98(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf108 module subroutine rkf108(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkc108 module subroutine rkc108(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkb109 module subroutine rkb109(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf1210 module subroutine rkf1210(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rkf1412 module subroutine rkf1412(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rko129 module subroutine rko129(me, t, x, h, xf, xerr)

module procedure /home/runner/work/rklib/rklib/doc/module/rklib_variable_steps.html rks1110a module subroutine rks1110a(me, t, x, h, xf, xerr)