APPLYING MULTIQUADRIC QUASI-INTERPOLATION TO SOLVE FOKKER-PLANCK EQUATION - Rahimi, M; Adibi, H; Amirfakhrian, M (TWMS journal of applied and engineering mathematics, 2023)
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 [Please download the PDF to view the formula] and collocation technique. Here, [theta]-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 [Please download the PDF to view the formula]. 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. Keywords: Fokker-Planck equation, multiquadric quasi-interpolation, [theta]-weighted finite difference method, collocation method, meshless method. AMS Subject Classification: 35Q84, 65M06.