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KraZug
KraZug
04:57
@xiaohuamao, to be honest I'm not an expert in the pure maths background. The introduction was written by my PhD supervisor, I used the technique in my thesis and then used it again last year.
Take a look at http://www.macs.hw.ac.uk/~simonm/talks/strath.pdf, and the paper https://gdz.sub.uni-goettingen.de/id/PPN243919689_0410?tify=%7B%22view%22:%22info%22,%22pages%22:%5B171%5D%7D
You don't discretize directly is the reason that spurious solutions tend not to occur in the same way
Yes, you do in solving the ODE, but not directly into a matrix form
The Compound Matrix Method part takes the differential equation underlying the Evans function and lifts it into a higher dimensional manifold (Grassmanian). This helps stop the unstable manifolds from dominating the numerical integration
But your second order equation doesn't use that anyway.
xiaohuamao
xiaohuamao
06:00
@KraZug Thanks. Does the method only work for linear ODE system?
 
1 hour later…
xiaohuamao
xiaohuamao
07:22
@KraZug The links are helpful. Thank you for sharing them. 'higher dimensional manifold', could you elaborate a bit more? What is this manifold? Solution manifold of the phi's in the intro pdf? By 'higher dimension', do you mean that the matrix A of phi's is larger than the matrix A of original y's? Or I misunderstand?
 
1 hour later…
KraZug
KraZug
08:27
@xiaohuamao, my implementation requires a linear ODE, not sure whether the Evans function can be used in nonlinear, probably not.
Yes, the phi matrix is larger than the original matrix, it is size n choose 2 instead of n

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