mrkiss_solvers_nt.f90 File Reference

RK Solvers. More...

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Data Types
interface	mrkiss_solvers_nt::deq_iface
	Type for ODE dydt functions. More...
interface	mrkiss_solvers_nt::stepp_iface
	Type step processing subroutine. More...
interface	mrkiss_solvers_nt::sdf_iface
	Type SDF function on a solution point. More...

Modules
module	mrkiss_solvers_nt
	Solvers.

Functions/Subroutines
One Step Solvers
subroutine, public	mrkiss_solvers_nt::step_all (status, y_deltas, dy, deq, y, param, a, b, c, t_delta)
	Compute one step of a embedded Runge-Kutta method expressed as a Butcher Tableau.
subroutine, public	mrkiss_solvers_nt::step_one (status, y_delta, dy, deq, y, param, a, b, c, t_delta)
	Compute one step of a Runge-Kutta method expressed as a Butcher Tableau.
subroutine, public	mrkiss_solvers_nt::step_richardson (status, y_delta, dy, deq, y, param, a, b, c, p, t_delta)
	Compute one Richardson Extrapolation Step.
One Step Test Solvers
subroutine, public	mrkiss_solvers_nt::step_rk4 (status, y_delta, dy, deq, y, param, t_delta)
	Compute one step of RK4 – the classical 4th order Runge-Kutta method (mrkiss_erk_kutta_4).
subroutine, public	mrkiss_solvers_nt::step_rkf45 (status, y_deltas, dy, deq, y, param, t_delta)
	Compute one step of RKF45 (mrkiss_eerk_fehlberg_4_5).
subroutine, public	mrkiss_solvers_nt::step_dp54 (status, y_deltas, dy, deq, y, param, t_delta)
	Compute one step of DP45 (mrkiss_eerk_dormand_prince_5_4)
Multistep Solvers
subroutine, public	mrkiss_solvers_nt::fixed_t_steps (status, istats, solution, deq, y, param, a, b, c, p_o, max_pts_o, t_delta_o, t_end_o, t_max_o)
	Take multiple fixed time steps with a simple Runge-Kutta method.
subroutine, public	mrkiss_solvers_nt::fixed_y_steps (status, istats, solution, deq, y, param, a, b, c, y_delta_len_targ, t_delta_max, t_delta_min_o, y_delta_len_tol_o, max_bisect_o, no_bisect_error_o, y_delta_len_idxs_o, max_pts_o, y_sol_len_max_o, t_max_o)
	Take multiple adaptive steps with constant \(\mathbf{\Delta{y}}\) length using a simple Runge-Kutta method.
subroutine, public	mrkiss_solvers_nt::sloppy_fixed_y_steps (status, istats, solution, deq, y, param, a, b, c, y_delta_len_targ, t_delta_ini, t_max_o, t_delta_min_o, t_delta_max_o, y_delta_len_idxs_o, adj_short_o, max_pts_o, y_sol_len_max_o)
	Take multiple adaptive steps adjusting for the length of \(\mathbf{\Delta{y}}\) using a simple Runge-Kutta method.
subroutine, public	mrkiss_solvers_nt::adaptive_steps (status, istats, solution, deq, y, param, a, b, c, p, t_max_o, t_end_o, t_delta_ini_o, t_delta_min_o, t_delta_max_o, t_delta_fac_min_o, t_delta_fac_max_o, t_delta_fac_fdg_o, error_tol_abs_o, error_tol_rel_o, max_pts_o, max_bisect_o, no_bisect_error_o, sdf_o, sdf_tol_o, stepp_o)
	Take multiple adaptive steps with an embedded Runge-Kutta method using relatively traditional step size controls.
Multistep Meta Solvers
subroutine, public	mrkiss_solvers_nt::fixed_t_steps_between (status, istats, solution, deq, y, param, a, b, c, steps_per_pnt, p_o)
	Take a solution with \(t\) values pre-populated, and take steps_per_pnt Runge-Kutta steps between each \(t\) value.
subroutine, public	mrkiss_solvers_nt::interpolate_solution (status, istats, solution, src_solution, deq, param, num_src_pts_o, linear_interp_o)
	Create an interpolated solution from a source solution.

Detailed Description

RK Solvers.

Author

Mitch Richling http://www.mitchr.me/

Keywords

runge kutta embedded butcher tableau

Standards

F2023

See also

https://github.com/richmit/MRKISS

Copyright

Copyright (c) 2025, Mitchell Jay Richling http://www.mitchr.me/ All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions, and the following disclaimer in the documentation and/or other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Definition in file mrkiss_solvers_nt.f90.