Out of the solvers available like MUMPS, PARADISO, SPOOLES, etc. which is best suited for solving highly non-linear problems
As i heard from my colleague that spooles is suited for this types of problems although i didnt work on this kind of problem yet.
I would recommend to you the Back Shoting Method. It works fine for highly non - linear problems. I attached the file for your convinience.
B-Spline method is best yet.
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