A unified approach for the solution of the Fokker-Planck equation

This paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the Fokker-Planck equation . The unified features of the discrete singular convolution algorithm are d iscussed. It is demonstrated that different implementations of the present algorithm, such as global, local, Galerkin, collocation and finite differen ce, can be deduced from a single starting point. Three benchmark stochastic systems, the repulsive Wong process, the Black-Scholes equation and a genu ine nonlinear model, are employed to illustrate the robustness and to test the accuracy of the present approach for the solution of the Fokker-Planck equation via a time-dependent method. An additional example, the incompress ible Euler equation, is used to further validate the present approach for m ore difficult problems. Numerical results indicate that the present unified approach is robust and accurate for solving the Fokker-Planck equation.