% Igor Yanovsky
% Teaching Assistant
% Math 151B
% 03/06/07

%#####################################################################
%
% This program solves the ordinary differential equation
% 
%  dy/dt = -y + t + 1,    0 <= t <= 5
%  y(0) = 1
% 
% using Euler's method. The function defining the ODE is defined in a
% separate Matlab function.
%
% This program also finds the error of the approximation by comparing the
% approximate solution and the exact solution  y(t) = exp(-t)+t.
% 
%#####################################################################

clear all

format long

% ODE Specification
%

t0 = 0.0;
tF = 5.0;
y0 = 1.0;

h = 0.1             % timestep
N = (tF-t0)/h       % number of timesteps

tn = t0;
wn = y0;

for(i=1:N)
    wnp1 = wn + h*f(wn,tn); % advances the ODE one step using Euler's method
    wn = wnp1;
    tn = tn + h;
end

wn
tn

yexact = exp(-tn) + tn
error = wn - yexact

fprintf(1,'N = %2d',N);  fprintf(1,', h = %4.2f',h);
fprintf(1,', w = %15.8e', wn);  fprintf(1,'\n');
   
clear all