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doc: Wrap m-file docstrings to 79 characters + newline (80 total).
* isrecording.m, soundsc.m, delaunay3.m, cell2mat.m, cumtrapz.m, del2.m,
inputParser.m, interp1.m, interp3.m, narginchk.m, profile.m,
validateattributes.m, delaunayn.m, tsearchn.m, voronoin.m, brighten.m,
cmunique.m, colorcube.m, imfinfo.m, imshow.m, edit.m, orderfields.m, run.m,
warning_ids.m, ode23.m, ode45.m, odeget.m, integrate_adaptive.m, kahan.m,
ode_struct_value_check.m, runge_kutta_23.m, fminunc.m, fsolve.m, fzero.m,
pkg.m, build.m, specular.m, view.m, bar.m, barh.m, contour3.m, isosurface.m,
line.m, pie.m, pie3.m, quiver3.m, scatter.m, scatter3.m, stem3.m, stemleaf.m,
surfl.m, tetramesh.m, isfigure.m, mkpp.m, pchip.m, residue.m, splinefit.m,
rmpref.m, unique.m, eigs.m, ilu.m, factor.m, factorial.m, gallery.m, hankel.m,
histc.m, ols.m, finv.m, fpdf.m, kruskal_wallis_test.m, weekday.m:
Wrap m-file docstrings to 79 characters + newline (80 total).
author | Rik <rik@octave.org> |
---|---|
date | Sun, 27 Mar 2016 15:50:01 -0700 |
parents | 8880d93010d8 |
children | 74257c267c8b |
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## Copyright (C) 2013-2015, Jacopo Corno <jacopo.corno@gmail.com> ## Copyright (C) 2013-2015, Roberto Porcu' <roberto.porcu@polimi.it> ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {} {[@var{t_next}, @var{x_next}] =} runge_kutta_23 (@var{@fun}, @var{t}, @var{x}, @var{dt}) ## @deftypefnx {} {[@var{t_next}, @var{x_next}] =} runge_kutta_23 (@var{@fun}, @var{t}, @var{x}, @var{dt}, @var{options}) ## @deftypefnx {} {[@var{t_next}, @var{x_next}] =} runge_kutta_23 (@var{@fun}, @var{t}, @var{x}, @var{dt}, @var{options}, @var{k_vals_in}) ## @deftypefnx {} {[@var{t_next}, @var{x_next}] =} runge_kutta_23 (@var{@fun}, @var{t}, @var{x}, @var{dt}, @var{options}, @var{k_vals_in}, @var{t_next}) ## @deftypefnx {} {[@var{t_next}, @var{x_next}, @var{x_est}] =} runge_kutta_23 (@dots{}) ## @deftypefnx {} {[@var{t_next}, @var{x_next}, @var{x_est}, @var{k_vals_out}] =} runge_kutta_23 (@dots{}) ## ## This function can be used to integrate a system of ODEs with a given initial ## condition @var{x} from @var{t} to @var{t+dt}, with the Bogacki-Shampine ## method of third order. For the definition of this method see ## @url{http://en.wikipedia.org/wiki/List_of_Runge%E2%80%93Kutta_methods}. ## ## @var{@fun} is a function handle that defines the ODE: @code{y' = f(tau,y)}. ## The function must accept two inputs where the first is time @var{tau} and ## the second is a column vector of unknowns @var{y}. ## ## @var{t} is the first extreme of integration interval. ## ## @var{x} is the initial condition of the system.. ## ## @var{dt} is the timestep, that is the length of the integration interval. ## ## The optional fourth argument @var{options} specifies options for the ODE ## solver. It is a structure generated by @code{odeset}. In particular it ## contains the field @var{funarguments} with the optional arguments to be used ## in the evaluation of @var{fun}. ## ## The optional fifth argument @var{k_vals_in} contains the Runge-Kutta ## evaluations of the previous step to use in a FSAL scheme. ## ## The optional sixth argument @var{t_next} (@code{t_next = t + dt}) specifies ## the end of the integration interval. The output @var{x_next} s the higher ## order computed solution at time @var{t_next} (local extrapolation is ## performed). ## ## Optionally the functions can also return @var{x_est}, a lower order solution ## for the estimation of the error, and @var{k_vals_out}, a matrix containing ## the Runge-Kutta evaluations to use in a FSAL scheme or for dense output. ## ## @seealso{runge_kutta_45_dorpri} ## @end deftypefn function [t_next, x_next, x_est, k] = runge_kutta_23 (f, t, x, dt, options = [], k_vals = [], t_next = t + dt) persistent a = [0 0 0; 1/2 0 0; 0 3/4 0]; persistent b = [0 1/2 3/4 1]; persistent c = [(2/9) (1/3) (4/9)]; persistent c_prime = [(7/24) (1/4) (1/3) (1/8)]; s = t + dt * b; cc = dt * c; aa = dt * a; k = zeros (rows (x), 4); if (! isempty (options)) # extra arguments for function evaluator args = options.funarguments; else args = {}; endif if (! isempty (k_vals)) # k values from previous step are passed k(:,1) = k_vals(:,end); # FSAL property else k(:,1) = feval (f, t, x, args{:}); endif k(:,2) = feval (f, s(2), x + k(:,1) * aa(2, 1).', args{:}); k(:,3) = feval (f, s(3), x + k(:,2) * aa(3, 2).', args{:}); ## compute new time and new values for the unkwnowns ## t_next = t + dt; x_next = x + k(:,1:3) * cc(:); # 3rd order approximation ## if the estimation of the error is required if (nargout >= 3) ## new solution to be compared with the previous one k(:,4) = feval (f, t_next, x_next, args{:}); cc_prime = dt * c_prime; x_est = x + k * cc_prime(:); endif endfunction