What is the error here? Euler Method for 2nd order equations?

I have the following files and script file, but the graph is definitely wrong for the approximations. Any ideas?

Code:

clear all

% define the problem: function f and domain
f = @(t,y) (0*t+3*y);
a = 0; b = 1;

% exact solution, using a fine grid
t = a:.0001:b;
y = exp(3*t); % this is a vector of values, not a function

% coarse solution
h = .25;
ya = 1;
[T1,Y1]=euler(f,a,b,ya,h);

% fine solution
h = .05;
ya = 1;
[T2,Y2]=euler(f,a,b,ya,h);

% finer solution
h = .01;
ya = 1;
[T3,Y3]=euler(f,a,b,ya,h);

plot(t,y,'k',T1,Y1,'bo-',T2,Y2,'ro-',T3,Y3,'go-')
legend('Exact','h=0.25','h=0.05','h=0.01')
title('The Euler Method with 3 meshes')

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(1) = a;
for k = 1 : length(T)-1
      Y(k+1) = Y(k) + h*f(T(k),Y(k));
end

[Walter Roberson]

Are you encountering an error message? What do you observe that leads you to be suspicious of the code?

Answer 1

[Torsten]

function[T,Y] = euler(f,a,b,ya,h)

a = 0; b = 1;

T = a:h:b;
Y = zeros(1,length(T));
*Y(1) = ya;*
for k = 1 : length(T)-1
      Y(k+1) = Y(k) + h*f(T(k),Y(k));
end

Best wishes

Torsten.

[Kaylene Widdoes]

So if I want to run the same code for (x^3)y' + 20(x^2)y = x, would I solve for dy/dx and then plug that equation in?

[Torsten]

Yes.

f = @(t,y) (t-20*t^2*y)/t^3;

Best wishes

Torsten.