% file: simpleEuler.m
% This matlab file will find the approximation to
%
% dy/dx = 1/y
% y(0) = starty
%
%
% To run this file you will first need to specify
% the step the following:
% h : the step size
% starty : the initial value
%
% The routine will generate three vectors. The first
% vector is x which is the grid points starting at
% x0=0 and have a step size h.
%
% The second vector is an approximation to the specified
% D.E.
%
% The third vector is the true solution to the D.E.
%
% If you haven't guessed, you cna use the percent sign
% to add comments.
%
x = [0:h:1];
y = 0*x;
y(1) = starty;
for i=2:max(size(y)),
y(i) = y(i-1) + h/y(i-1);
end
true = sqrt(2*x+1);