It depends on your system and non-linearity...
for example runge-kutta is suitable method for the equations are in state space or the Euler method is a first-order method and it's useful to first ordinary equations .these methods are numerical and convenient. but in the analytical methods, you can use perturbation , harmonic balance and volterra series,... .
Nice question. It seems to me, the problem, the type of nonlinearity and the severity of the nonlinearity, and even the response which is not at hand prior to the analysis and maybe the discretization in space (and even the computational facility affecting the round off) are important in the selection. In any way, before any precise response, it seems also important to know whether robustness, accuracy, or efficiency, or even something else is the most important issue for us. (In may problems, fractional time stepping seems robust but not efficient.) With many thanks for your kind attention to the lines above, as well as the nice question, and best wishes for all, have very nice hours ahead.
Thanks Aram Soroushian . This is quite difficult task to decide because there are several things associated with nonlinear model. So its not as straight forward as it looks.
The matrix decomposition of vector functions is suitable method for nonlinear analysis in state space.
We have proposed a numerical method (denoted as MEM) for solving the
Nonlinear Dynamic problems. If you would like, you can view our published articles in this field entitled "dynamic analysis of SDOF systems using modified energy method". By the way, the presented idea is also generalized to MDOF systems in another study, which is available on my research-gate account.
if you need more information, please let me know.
Regards,
Jalili
Hard to say. Let me give you an example. I had a nonlinear ODE and I used Maple to solve it. There are over 20 methods to solve ODEs in Maple. Just couple of them could solve the equation. The method is depend on your equation how much it is nonlinear? How your equation is stiff? Is your equation/s are bad behaviour? So it is not easy to answer your question.
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