Some Computational Methods for the Fokker–Planck Equation

Three computational techniques are proposed for the numerical solution of the Fokker–Planck equation (FPE): the semi-implicit Euler, implicit Euler, and Crank–Nicolson type methods. The types of equations considered includes the FPE with constant or linear drift coefficient, the backward Kolmogorov equation, and the non-linear FPE. Comparisons of the computed numerical results with the exact solutions for three examples has been performed to validate the proposed schemes, which prove competitive against existing methods.