Mercurial > forge
view extra/ode/rk2fixed.m @ 0:6b33357c7561 octave-forge
Initial revision
author | pkienzle |
---|---|
date | Wed, 10 Oct 2001 19:54:49 +0000 |
parents | |
children | a0d3391e59e2 |
line wrap: on
line source
function [tout,xout] = rk2fixed(F,tspan,x0,Nsteps,ode_fcn_format,trace,count) % Copyright (C) 2000 Marc Compere % This file is intended for use with Octave. % rk2fixed.m 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 2, or (at your option) % any later version. % % rk2fixed.m 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 at www.gnu.org/copyleft/gpl.html. % % -------------------------------------------------------------------- % % rk2fixed (v1.07) integrates a system of ordinary differential equations using a % 2nd order Runge-Kutta formula called Ralston's method. % This choice of 2nd order coefficients provides a minimum bound on truncation error. % For more, see Ralston & Rabinowitz (1978) or % Numerical Methods for Engineers, 2nd Ed., Chappra & Cannle, McGraw-Hill, 1985 % % rk2fixed() requires 2 function evaluations per integration step. % % Usage: % [tout, xout] = rk2fixed(F, tspan, x0, Nsteps, ode_fcn_format, trace, count) % % INPUT: % F - String containing name of user-supplied problem derivatives. % Call: xprime = fun(t,x) where F = 'fun'. % t - Time (scalar). % x - Solution column-vector. % xprime - Returned derivative COLUMN-vector; xprime(i) = dx(i)/dt. % tspan - [ tstart, tfinal ] % x0 - Initial value COLUMN-vector. % Nsteps - number of steps used to span [ tstart, tfinal ] % ode_fcn_format - this specifies if the user-defined ode function is in % the form: xprime = fun(t,x) (ode_fcn_format=0, default) % or: xprime = fun(x,t) (ode_fcn_format=1) % Matlab's solvers comply with ode_fcn_format=0 while % Octave's lsode() and sdirk4() solvers comply with ode_fcn_format=1. % trace - If nonzero, each step is printed. (optional, default: trace = 0). % count - if nonzero, variable 'rhs_counter' is initalized, made global % and counts the number of state-dot function evaluations % 'rhs_counter' is incremented in here, not in the state-dot file % simply make 'rhs_counter' global in the file that calls rk2fixed % % OUTPUT: % tout - Returned integration time points (row-vector). % xout - Returned solution, one solution column-vector per tout-value. % % The result can be displayed by: plot(tout, xout). % % Marc Compere % compere@mail.utexas.edu % created : 06 October 1999 % modified: 15 May 2000 if nargin < 7, count = 0; end if nargin < 6, trace = 0; end if nargin < 5, Nsteps = 400/(tspan(2)-tspan(1)); end % <-- 400 is a guess for a default, % try verifying the solution with rk4fixed if nargin < 4, ode_fcn_format = 0; end if count==1, global rhs_counter if ~exist('rhs_counter'),rhs_counter=0;,end end % if count % Initialization t = tspan(1); h = (tspan(2)-tspan(1))/Nsteps; xout(1,:) = x0'; tout(1) = t; x = x0(:); if trace clc, t, h, x end % The main loop h = (tspan(2)-tspan(1))/Nsteps; for i=1:Nsteps, if (ode_fcn_format==0), k1 = feval(F,t,x); k2 = feval(F,t+3/4*h,x+3/4*h*k1); else, k1 = feval(F,x,t); k2 = feval(F,x+3/4*h*k1,t+3/4*h); end % if (ode_fcn_format==0) % increment rhs_counter if count==1, rhs_counter = rhs_counter + 2; end % if t = t + h; x = (x+h*(1/3*k1+2/3*k2)); tout = [tout; t]; xout = [xout; x.']; if trace, home, t, h, x end end