Discrete singular convolution for the solution of the Fokker-Planck equation

摘要

This paper introduces a discrete singular convolution algorithm for solving the Fokker-Planck equation. Singular kernels of the Hilbert-type and the delta type are presented for numerical computations. Various sequences of approximations to the singular kernels are discussed. A numerical algorithm is proposed to incorporate the approximation kernels for physical applications. Three standard problems, the Lorentz Fokker-Planck equation, the bistable model and the Henon-Heiles system, are utilized to test the accuracy, reliability, and speed of convergency of the present approach. All results are in excellent agreement with those of previous methods in the field.