% EulerDriver.m

% This is a driver that inputs the appropriate 
% initial conditions and step size for using the
% function Euler.m to numerically solve the IVP given by
%   y' = f(t,y)   y(t0)=y0
% Note that the user must input the name of the function
% to be used to obtain function values for f(t,y)

% Clear the workspace
clear

% Set initial conditions
t0  = 0;
y0  = 0;

% Set step size and number of steps taken
h   = 0.1;
M   = 10; 

% name of the function containing the right-hand
% side of the ode.
%NOTE:  USER MUST EDIT THE FOLLOWING!!!!
name = 'h5num3';

% call Euler.m
[t_vec,y_vec] = Euler(name,h,M,t0,y0);

% t_vec is the vector of t-values from the step
% size given by h.
% y_vec is the corresponding approximations for the
% solution to the ivp.  We can plot the linear interpolant 
% of the approx. solution values along with the true solution 
% to compare.

t=[t0:h/10:t0 + M*h];              % gives us a fine set of grid
                                   % points for the plot
TrueSoln_vec = (t.*exp(3*t)-0.2*exp(3*t))/5+exp(-2*t)/25;

figure(1)
plot(t,TrueSoln_vec,'r-',t_vec,y_vec,'b*');
legend('True Solution','Euler, h = 0.1');
title('Homework 5, Number 3')
xlabel('t');
ylabel('y(t)');