Solving the Fokker-Planck equation via the compact finite difference method

In this study, we solve the Fokker-Planck equation by a compact finite difference method, By the finite difference method the computation of Fokker-Planck equation is reduced to a system of ordinary differential equations. Two different methods, boundary value method and cubic C1-spline collocation method, for solving the resulting system are proposed. Both methods have fourth-order accuracy in time variable. By the boundary value method, some pointwise approximate solutions are only obtained. But, C1-spline method gives a closed-form approximation in each space step, too. Illustrative examples are included to demonstrate the validity and efficiency of the methods. A comparison is made with existing results.