What possibilites does
NDSolve provide for solving partial differential equation using a pseudospectral method?
NDSolve provides the
"DifferenceOrder"->"Pseudospectral". As I understand the documentary the method is using some form of Chebyshev polynomials $T_n$ for the expansion of a function $f$ to solve the differential equation:
- Am I correct that
NDSolvereally uses a pseudospectral method here or is it just distribution the gridpoints in a different way and using FD?
- If so, which polynomials are used here exactly? How is the truncation $N$ defined?
- Which possibilities do I have to implement a pseudospectral method inherently in Mathematica's
NDSolve(if any) using standard polynomials (like Bessel Functions, Jacobi Polynomials etc)?