Binary spectral collocation method for the nonlinear Fokker-Planck equation

Abstract

A mixed Laguerre-Legendre spectral collocation schemes is constructed for initial-boundary value problem of the nonlinear Fokker-Planck nonhomogeneous equations and the linear Fokker-Planck homogeneous equation by using the Laguerre interpolation functions in velocity, and the Legendre interpolation functions in time, which is a bivariate Lagrange interpolation approximation function based on Legendre and Laguerre Gauss quadrature notes. The original problem is changed into a matrix equation and solved by Newton iteration. Numerical experiments show that the algorithm has high accuracy and efficiency.