Numerical solution of non-linear Fokker–Planck equation using finite differences method and the cubic spline functions

Abstract

In this paper we proposed a finite difference scheme for solving the nonlinear Fokker–Planck equation. We apply a finite difference approximation for discretizing spatial derivatives. Then we use the cubic C1-spline collocation method which is an A-stable method for the time integration of the resulting nonlinear system of ordinary differential equations. The proposed method has second-order accuracy in space and fourth-order accuracy in time variables. The numerical results confirm the validity of the method.