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

This paper introduces a discrete singular convolution algorithm for solving the Fokker-Planck equation. Singular kernels of the Hilbert-type and the d elta type are presented for numerical computations. Various sequences of ap proximations to the singular kernels are discussed. A numerical algorithm i s proposed to incorporate the approximation kernels for physical applicatio ns. Three standard problems, the Lorentz Fokker-Planck equation, the bistab le model and the Henon-Heiles system, are utilized to test the accuracy, re liability, and speed of convergency of the present approach. All results ar e in excellent agreement with those of previous methods in the field. (C) 1 999 American Institute of Physics. [S0021-9606(99)50518-7].