% Uses Euler's method to compute numerical solution to the ode
%  y'=f(t,y)  y(a)=alpha   a<=t<=b.
% Asks user to input a,b,step size h and initial value alpha
% Assumes f is evaluated in a separate function file f.m
% Plots the result with discrete points. 

a=input('Please enter the left endpoint:');
b=input('Please enter the right endpoint:');
h=input('Please enter the step size');
n=ceil((b-a)/h);
alpha=input('Please enter the initial value:');
clear t w 
t=a:h:(a+n*h);
w(1)=alpha;

for i=1:n
  w(i+1)=w(i)+h*f(t(i),w(i));
end

hold off
plot(t,w,'*');


%For the example y'=y^2-t^2+1 y(0)=0.5 
% here we now plot the true solution alongside the 
% approximation.
%hold on
%tvals=a:0.01:b;
%plot(tvals,1+tvals.^2+2*tvals-0.5*exp(tvals));
%plot(tvals,exp(-50*tvals));