Euler method is coming up wrong? Help?

I have the following equation: (x^3)y' + 20*(x^2)y = x with y(2)=0
I have to get the Euler code to run and execute. So far this is my code, but the graph looks wrong, and the approximations aren't even showing up. Any ideas why this may be happening?
Script file:
function[T,Y] = euler(f,a,b,ya,h)
a = 0; b = 1;
T = a:h:b;
Y = zeros(1,length(T));
Y(2) = ya;
for k = 1 : length(T)-1
Y(k+1) = Y(k) + h*f(T(k),Y(k));
end
Code:
%%Part 1 - Euler
% y'(t) = 3*y(t)
% A function file euler.m is needed; you'll do this in the homework
clear all
% define the problem: function f and domain
f = @(t,y) (1/(t^2)) - ((20*y)/t);
a = 2; b = 10;
% exact solution, using a fine grid
t = a:.0001:b;
y = (1./(19.*t)) - (524288./(19.*(t.^20))); % this is a vector of values, not a function
% coarse solution
h = .01;
ya = 0;
[T1,Y1]=euler(f,a,b,ya,h);
% fine solution
h = .001;
ya = 0;
[T2,Y2]=euler(f,a,b,ya,h);
% finer solution
h = .0001;
ya = 0;
[T3,Y3]=euler(f,a,b,ya,h);
plot(t,y,'k',T1,Y1,'bo-',T2,Y2,'ro-',T3,Y3,'go-')
legend('Exact','h=0.01','h=0.001','h=0.001')
title('The Euler Method with 3 meshes')

1 Comment

Kaylene - please don't create a duplicate of previously asked questions (<http://www.mathworks.com/matlabcentral/answers/268698-any-ideas-why-euler-method-isn-t-running>).

Answers (0)

This question is closed.

Asked:

on 17 Feb 2016

Closed:

on 17 Feb 2016

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