rk_fixed_step_class Derived Type

type, public, abstract, extends(rk_class) :: rk_fixed_step_class

fixed step size class


Inherits

type~~rk_fixed_step_class~~InheritsGraph type~rk_fixed_step_class rk_fixed_step_class type~rk_class rk_class type~rk_fixed_step_class->type~rk_class root_method root_method type~rk_class->root_method solver

Inherited by

type~~rk_fixed_step_class~~InheritedByGraph type~rk_fixed_step_class rk_fixed_step_class type~euler_class euler_class type~euler_class->type~rk_fixed_step_class type~heun_class heun_class type~heun_class->type~rk_fixed_step_class type~midpoint_class midpoint_class type~midpoint_class->type~rk_fixed_step_class type~rk3_class rk3_class type~rk3_class->type~rk_fixed_step_class type~rk4_class rk4_class type~rk4_class->type~rk_fixed_step_class type~rk5_class rk5_class type~rk5_class->type~rk_fixed_step_class type~rk7_class rk7_class type~rk7_class->type~rk_fixed_step_class type~rk8_10_class rk8_10_class type~rk8_10_class->type~rk_fixed_step_class type~rk8_12_class rk8_12_class type~rk8_12_class->type~rk_fixed_step_class type~rkb6_class rkb6_class type~rkb6_class->type~rk_fixed_step_class type~rkc5_class rkc5_class type~rkc5_class->type~rk_fixed_step_class type~rkcv8_class rkcv8_class type~rkcv8_class->type~rk_fixed_step_class type~rkh10_class rkh10_class type~rkh10_class->type~rk_fixed_step_class type~rkl5_class rkl5_class type~rkl5_class->type~rk_fixed_step_class type~rklk5a_class rklk5a_class type~rklk5a_class->type~rk_fixed_step_class type~rklk5b_class rklk5b_class type~rklk5b_class->type~rk_fixed_step_class type~rkls44_class rkls44_class type~rkls44_class->type~rk_fixed_step_class type~rkls54_class rkls54_class type~rkls54_class->type~rk_fixed_step_class type~rko10_class rko10_class type~rko10_class->type~rk_fixed_step_class type~rkr4_class rkr4_class type~rkr4_class->type~rk_fixed_step_class type~rks10_class rks10_class type~rks10_class->type~rk_fixed_step_class type~rks4_class rks4_class type~rks4_class->type~rk_fixed_step_class type~rks5_class rks5_class type~rks5_class->type~rk_fixed_step_class type~rkssp22_class rkssp22_class type~rkssp22_class->type~rk_fixed_step_class type~rkssp33_class rkssp33_class type~rkssp33_class->type~rk_fixed_step_class type~rkssp53_class rkssp53_class type~rkssp53_class->type~rk_fixed_step_class type~rkssp54_class rkssp54_class type~rkssp54_class->type~rk_fixed_step_class type~rkz10_class rkz10_class type~rkz10_class->type~rk_fixed_step_class

Type-Bound Procedures

procedure, public :: destroy

destructor

  • private subroutine destroy(me)

    Destructor for rk_class.

    Arguments

    Type IntentOptional Attributes Name
    class(rk_class), intent(out) :: me

procedure, public :: stop => rk_class_stop

user-callable method to stop the integration

  • private subroutine rk_class_stop(me)

    User-callable method to stop the integration (e.g., from f, g, or report). No further function evaluations are done, and the integrator returns, with the status set to RKLIB_ERROR_USER_STOPPED. This is not treated as an error (i.e., it does not stop the program if stop_on_errors is true).

    Arguments

    Type IntentOptional Attributes Name
    class(rk_class), intent(inout) :: me

procedure, public :: status => rk_class_status

get status code and message

  • private subroutine rk_class_status(me, istatus, message)

    Get the status of an integration.

    Arguments

    Type IntentOptional Attributes Name
    class(rk_class), intent(in) :: me
    integer, intent(out), optional :: istatus

    status code (<0 means an error)
    character(len=:), intent(out), optional, allocatable :: message

    status message

procedure, public :: failed

  • private function failed(me)

    Returns true if there was an error. Can use rk_class_status to get more info.

    Arguments

    Type IntentOptional Attributes Name
    class(rk_class), intent(in) :: me

    Return Value logical

procedure, public :: interpolate

dense output for the last accepted step

  • private recursive subroutine interpolate(me, t, x, istatus)

    Dense output: compute the state at a time within the last accepted step, using the continuous extension of the method (if it has one, see rklib_properties dense).

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(rk_class), intent(inout) :: me
    real(kind=wp), intent(in) :: t

    time at which to compute the state
    real(kind=wp), intent(out), dimension(me%n) :: x

    state at t
    integer, intent(out), optional :: istatus

    status of this call

procedure, public :: dense_interval

interval of the last accepted step for the dense output

  • private subroutine dense_interval(me, available, t0, tf, x0, xf)

    Returns the interval of the last accepted step, which is where interpolate can be used. For example, this can be called from the report function to get the previous time and state, so that points in between can be computed.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(rk_class), intent(inout) :: me
    logical, intent(out) :: available

    if dense output is available
    real(kind=wp), intent(out), optional :: t0

    initial time of the step
    real(kind=wp), intent(out), optional :: tf

    final time of the step
    real(kind=wp), intent(out), optional, dimension(me%n) :: x0

    initial state of the step
    real(kind=wp), intent(out), optional, dimension(me%n) :: xf

    final state of the step

procedure(properties_func), public, deferred :: properties

  • pure function properties_func(me) result(p) Prototype

    Returns the properties of the method.

    Arguments

    Type IntentOptional Attributes Name
    class(rk_class), intent(in) :: me

    Return Value type(rklib_properties)

    properties of the method

procedure(step_func_fixed), private, deferred :: step

the step routine for the rk method

  • subroutine step_func_fixed(me, t, x, h, xf) Prototype

    rk step function for the fixed-step methods.

    Arguments

    Type IntentOptional Attributes Name
    class(rk_fixed_step_class), intent(inout) :: me
    real(kind=wp), intent(in) :: t

    initial time
    real(kind=wp), intent(in), dimension(me%n) :: x

    initial state vector
    real(kind=wp), intent(in) :: h

    time step

    real(kind=wp), intent(out), dimension(me%n) :: xf

    final state vector

procedure, public :: initialize => initialize_fixed_step

initialize the class (set n,f, and report)

  • private subroutine initialize_fixed_step(me, n, f, report, g, stop_on_errors, max_number_of_steps, report_rate, solver)

    Initialize the rk_fixed_step_class.

    Arguments

    Type IntentOptional Attributes Name
    class(rk_fixed_step_class), intent(inout) :: me
    integer, intent(in) :: n

    number of variables
    procedure(deriv_func) :: f

    derivative function
    procedure(report_func), optional :: report

    for reporting the steps
    procedure(event_func), optional :: g

    for stopping at an event
    logical, intent(in), optional :: stop_on_errors

    stop the program for any errors (default is False)
    integer, intent(in), optional :: max_number_of_steps

    max number of steps allowed
    integer, intent(in), optional :: report_rate

    how often to call report function: 0 : no reporting (same as not associating report), 1 : report every point, 2 : report every other point, etc. The first and last point are always reported.
    class(root_method), intent(in), optional :: solver

    the root-finding method to use for even finding. if not present, then brent_solver is used.

procedure, public :: integrate => integrate_fixed_step

  • private subroutine integrate_fixed_step(me, t0, x0, h, tf, xf)

    Main integration routine for the rk_class.

    Arguments

    Type IntentOptional Attributes Name
    class(rk_fixed_step_class), intent(inout) :: me
    real(kind=wp), intent(in) :: t0

    initial time
    real(kind=wp), intent(in), dimension(:) :: x0

    initial state
    real(kind=wp), intent(in) :: h

    abs(time step)
    real(kind=wp), intent(in) :: tf

    final time
    real(kind=wp), intent(out), dimension(:) :: xf

    final state

procedure, public :: integrate_to_event => integrate_to_event_fixed_step

  • private subroutine integrate_to_event_fixed_step(me, t0, x0, h, tmax, tol, tf, xf, gf)

    Event-finding integration routine for the rk_class. Integrates until g(t,x)=0, or until t=tf (whichever happens first).

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(rk_fixed_step_class), intent(inout) :: me
    real(kind=wp), intent(in) :: t0

    initial time
    real(kind=wp), intent(in), dimension(:) :: x0

    initial state
    real(kind=wp), intent(in) :: h

    abs(time step)
    real(kind=wp), intent(in) :: tmax

    max final time if event not located
    real(kind=wp), intent(in) :: tol

    function tolerance for root finding
    real(kind=wp), intent(out) :: tf

    actual final time reached
    real(kind=wp), intent(out), dimension(:) :: xf

    final state (at tf)
    real(kind=wp), intent(out) :: gf

    g value at tf

procedure, private :: begin_integration => begin_integration_rk_fixed_step_class

Source Code

    type,extends(rk_class),abstract,public :: rk_fixed_step_class

        !! fixed step size class

        private

        contains

        private

        procedure(step_func_fixed),deferred :: step !! the step routine for the rk method
        procedure,public :: initialize => initialize_fixed_step !! initialize the class (set n,f, and report)

        procedure,public :: integrate => integrate_fixed_step
        procedure,public :: integrate_to_event => integrate_to_event_fixed_step
        procedure :: begin_integration => begin_integration_rk_fixed_step_class

    end type rk_fixed_step_class