Numerical Solution of Time Fractional Stochastic Korteweg-de Vries Equation via Implicit Meshless Approach

In this article, a numerical scheme is implemented to approximate the solution of time fractional stochastic Korteweg-de Vries (KdV) equation. The structure of the proposed method is such that it first employ finite difference technique to transform the time fractional stochastic KdV equation into elliptic stochastic differential equations (SDEs). Then resulting elliptic SDEs has been estimated via a meshless method based on radial basis functions (RBFs). It should be mentioned that every RBFs with sufficient smoothness can be applied. In this paper, we use Gaussian RBFs which are infinitely smoothness to approximate the functions in the resulting elliptic SDEs. The most important advantage of proposed method respect to traditional numerical method is that the noise terms are directly simulated at the collocation points in each step time. Finally, some test problems are presented to investigate the performance and accuracy of the new method.