Solving one‐dimensional nonlinear stochastic Sine‐Gordon equation with a new meshfree technique

다국어 초록 (Multilingual Abstract)

In the current work, we consider the nonlinear one‐dimensional stochastic Sine‐Gordon equation with appropriate initial and boundary conditions. The main goal of this work is presenting a numerical scheme based on radial basis functions (RBFs) and finite difference method to provide the approximate solution of mentioned equation. For approximating the solution, finite difference idea is used to overcome the time variable and then strictly positive definite RBFs such as Gaussian have been used to estimate the unknown function in time step n. Finally, several examples are given to check the accuracy and efficiency of the provided solution.