eulode.m

function [t,y] = eulode(dydt,tspan,y0,h,varargin)
% eulode: Euler ODE solver
%   [t,y] = eulode(dydt,tspan,y0,h,p1,p2,...):
%           uses Euler's method to integrate an ODE
% input:
%   dydt = name of the M-file that evaluates the ODE
%   tspan = [ti, tf] where ti and tf = initial and
%   final values of independent variable
%   y0 = initial value of dependent variable
%   h = step size
%   p1,p2,... = additional parameters used by dydt
% output:
%   t = vector of independent variable
%   y = vector of solution for dependent variable
if nargin<4,error('at least 4 input arguments required'),end
ti = tspan(1);tf = tspan(2);
if ~(tf>ti),error('upper limit must be greater than lower'),end
t = (ti:h:tf)'; n = length(t);
% if necessary, add an additional value of t
% so that range goes from t = ti to tf
if t(n)<tf
  t(n+1) = tf;
  n = n+1;
end
y=zeros(n,length(y0));
y(1,:)=y0;
for i = 1:n-1 %implement Euler's method
  y(i+1,:) = y(i,:) + dydt(t(i),y(i,:),varargin{:})'*(t(i+1)-t(i));
end