Applying multiquadric quasi-interpolation to solve Fokker-Planck equation

Abstract

The Fokker-Planck equation (FPE) arises in various fields in physics, chemistry, natural science. It is difficult to obtain analytical solutions, accordingly we resort to numerical methods. In this study, we present a meshfree method to solve FPE. It is based on the multiquadric quasi-interpolation (MQQI) operator LW2 and collocation technique. Here, ?-weighted finite difference scheme is used to discretize the temporal derivative. Then, the unknown function and its spatial derivatives are approximated by the multiquadric quasi-interpolation (MQQI) operator LW2. Furthermore, the stability of the technique is investigated. This method is applied to some examples and the numerical results have been compared with the exact solutions and results of another method.