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Does anyone know the procedure (or have pseudo code) to approximating the largest eigenvalue of a monodromy matrix? Or even to approximate the monodromy matrix itself?

There is no explicit solution to acquire the fundamental matrix in this case.

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If you can afford the CPU time and storage, compute the monodromy matrix explicitly by solving $n$ IVPs with the vectors of the canonical basis.

Otherwise, use Arnoldi, possibly in the default functions included in your computing environment (e.g., Matlab's eigs, or scipy.sparse.linalg.eigs), providing a callback function that evaluates f(v)=Av by solving an IVP.

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  • $\begingroup$ Thanks, I'm using Matlab so eigs will hopefully do it. I'm just a bit confused on how to calculate the matrix in the first place. I'm not completely familiar with this stuff, I've been following theexample linked below. imgur.com/DJyZOxN From my understanding you need to factor out constants to obtain the fundemental matrix, is there a way of calculating it when MATLAB is telling me there's no explicit solution? $\endgroup$
    – Aidan2160
    Jun 18, 2016 at 12:04
  • $\begingroup$ @Aidan2160 If you want to follow the Arnoldi approach, you don't need to compute the matrix, but you give Matlab a procedure that computes its action (see the examples with Afun on it.mathworks.com/help/matlab/ref/…). If you have doubts with definitions and basic facts about monodromy matrices, I am afraid that Mathoverflow is not the right place to ask about it. $\endgroup$ Jun 18, 2016 at 17:41
  • $\begingroup$ I've been having a lot of trouble with this. I know this isn't the best thing to ask on here, but could I pay you to write up this code. Could pay 50 euro and send on the information by email. It seems like it should take 30 minutes to do $\endgroup$
    – Aidan2160
    Jun 19, 2016 at 13:41

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