Problem with second order ODE solver

Hello everybody,

I'm trying to solve the following equation: y" = sin(y) - (1/t)*y'

I write down the following code for solving the equation but the output does not show anything, do i miss something here?

syms y(t)

[V] = odeToVectorField(diff(y, 2) == sin(y)-(1/t)*diff(y))

M = matlabFunction(V,'vars', {'t','Y'})

sol = ode45(M,[0 30],[5.71 0])

fplot(@(x)deval(sol,x,1), [0, 30])

I really appreciate your help!

Thanks.

Answer 1

[Star Strider]

The problem is having ‘t’ to include 0 and having ‘t’ in the denominator. This creates a ‘0/0’ condition that equates to NaN, and tha then propagates throughout the integration of your ODE.

The easiest way to avoid that problem is to ‘cheat’, and use eps instead of 0.

This works:

syms y(t)
[V] = odeToVectorField(diff(y, 2) == sin(y)-(1/t)*diff(y))
M = matlabFunction(V,'vars', {'t','Y'})

[T,Y] = ode45(M,[eps 30],[5.71 0]);

figure(1)
plot(T, Y)
grid

[Yas]

Thank you very much! Yes it worked. However I have one more question: 1. why the new code generates to separate plots (orange and blue)? I mean the solution to this eq should be one right?

[Star Strider]

My pleasure!

There are two outputs (columns) in ‘Y’, ‘Y(:,1)’ (the derivative) and ‘Y(:,2)’, the solved equation. If you only want the solved equation, the plot changes to:

figure(1)
plot(T, Y(:,2))
grid