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I am facing a problem solving a ODE with a Runge-Kutta 4th order method:

The expression in order to solve is :

\begin{equation} Ay^{''}+By^{'}+Cy= Cu \end{equation}

\begin{equation} y =OUTPUT \end{equation}

\begin{equation} u=INPUT \end{equation}

We are using a sample time of 0.01s (with 0.001s sample time it does work), but the solver with some combinations of A,B and C does not converge. Then, we would like to know these combinations of A,B and C that make the method fail before start to using it.

Thanks in advance.

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    $\begingroup$ Whenever you have $ B^2-4AC<0$ you'd have better luck with a predictor corrector method. The short answer is because your solution is "oscillating". $\endgroup$
    – Jeb
    Commented Jul 28, 2015 at 12:01

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Here is the complete answer.

https://math.stackexchange.com/questions/1376678/runge-kutta-stability/1376710#1376710

Sorry for the duplication.

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