rkls54_class Derived Type

type, public, extends(rk_fixed_step_class) :: rkls54_class

5-stage, 4th order low storage Runge-Kutta Carpenter-Kennedy


Inherits

type~~rkls54_class~~InheritsGraph type~rkls54_class rkls54_class type~rk_fixed_step_class rk_fixed_step_class type~rkls54_class->type~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

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, 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, public :: step => rkls54

  • interface

    private module subroutine rkls54(me, t, x, h, xf)

    Arguments

    Type IntentOptional Attributes Name
    class(rkls54_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

procedure, public :: properties => rkls54_properties

  • interface

    private pure module function rkls54_properties(me) result(p)

    Arguments

    Type IntentOptional Attributes Name
    class(rkls54_class), intent(in) :: me

    Return Value type(rklib_properties)

    properties of the method