Non-linear ordinary differential equation is some time not solvable. There solution is not known. Can anyone suggest a method for there solution?
Pseudospectral method can be used when our exact solutions be smooth or have suitable regularity, but for nonsmooth solutions spectral element method must be applied.
Yes, pseudo spectral method is always faster and highly accurate. If you have periodic boundaries then go with the Fourier spectral method.
Pseudospectral method can be used when our exact solutions be smooth or have suitable regularity, but for nonsmooth solutions spectral element method must be applied.
Yes indeed, pseudo spectral methods are usually used to approximate the solution of nonlinear ODEs.
It depends on the behaviour of the solution. For smooth problems, yes, global spectral methods are the best / most efficient way you can do, either through Galerkin or collocation. However, if the solution is non-smooth, a global method will get you into trouble and will require additional stabilization through filtering or other measures.
Yes one can apply pseudo-spectral or other methods such as Galerkin's method , B-spline collocation method etc to solve a non-linear ODE. As rightly pointed out , one should see type of domain, boundary conditions and non-linearity in the equation so that it can be tackled. One may use quasilinearisation to linearise non-linear terms.
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