APPLYING MULTIQUADRIC QUASI-INTERPOLATION TO SOLVE FOKKER-PLANCK EQUATION

APPLYING MULTIQUADRIC QUASI-INTERPOLATION TO SOLVE FOKKER-PLANCK EQUATION

M. Rahimi, H. Adibi, M. Amirfakhrian

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Abstract

The Fokker-Planck equation (FPE) arises in various  elds in physics, chem- istry, natural science. It is di cult 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  nite di erence 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 stabil- ity 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.

Keywords

Fokker-Planck equation, multiquadric quasi-interpolation,  -weighted  nite di erence method, collocation method, meshless method.