Optimization of the shape parameter of RBF based on the PSO algorithm to solve nonlinear stochastic differential equation

In this paper, the Particle Swarm Optimization (PSO) is used to determine a good shape parameter of meshfree method with radial basis function (RBF) to get distribution function of Fokker-Planck equation associated to nonlinear stochastic differential equations. Numerical procedures based on Kansa’s method and particle swarm optimization are applied to Duffing oscillator model. This paper gives the best shape parameter by PSO by minimizing the Root Mean Square Error (RMSE). The effectiveness of the method is demonstrated and the obtained results are well compared to the available ones.