Using ODE, several errors with a spring system and function

I am attempting to set up a function file for the following differential equation: (u''+ u + epsilon*u^3 = 0) with initial conditions: u(0) = 0, u'(0) = 1.

My variables are t, epsilon, and u, so my code for my function is:

function [ du ] = fu( t,e,u )
    du= zeros(2,1);
    du(1)= u(2);
    du(2)= -(u(1))-e*(u(1))^3;
end
saved as 'F1'

when I run:

e=[0.0:.2:1.0]
t=[1 20]
ic=[0 1]
[T, U]=ode45('F1',t,e,ic)

I get a huge series of errors starting with: Attempted to access u(2); index out of bounds because numel(u)=0.

Error in F1 (line 3)
    du(1)= u(2);

Please help me! I have no clue why this is not working and I'm extremely stuck.

[James Tursa]

What is the purpose of e being a vector? Are you trying to solve the ODE multiple times for multiple values of epsilon? Do you need help with how to pass that epsilon value into your F1 routine?

[Robert Fennis]

Have you saved all of your latest files? Also make sure the function fu has the same name as your file. I don't know if this causes the problem but you are not supposed to mix those up. Also, I see that they use a different syntax in the examples:

 [t,y] = ode45(@vdp1,[0 20],[2; 0]);

Answer 1

[Mischa Kim]

Julia, use

function myODE()
e  = 0.0:.2:1.0;     % no brackets, the colons are used to define the vector
t  = [1 20];
ic = [0; 1];         % column (not row) vector
for ii = 1:numel(e)  % I guess you want to solve for different e?
    [T, U] = ode45(@fu,t,ic,[],e(ii));
    hold on
    plot(T,U)
end
end

function [du] = fu(~,u,e)
du = [u(2); -(u(1))-e*(u(1))^3]; % like above, column not row vector
end

Put the code above into one .m file, name it myODE.m and run.