Solving one‐dimensional nonlinear stochastic Sine‐Gordon equation with a new meshfree technique. (23rd December 2020)

• Record Type: Journal Article
• Authors: Mirzaee, Farshid; Rezaei, Shadi; Samadyar, Nasrin
• Is Part Of: International journal of numerical modelling. Volume 34:Number 4(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-12-23
• Subjects: Brownian motion process -- one‐dimensional stochastic Sine‐Gordon equation -- radial basis function -- stochastic partial differential equations; Electric networks -- Mathematical models -- Periodicals; Electronics -- Mathematical models -- Periodicals; 621.3011
• DOI: 10.1002/jnm.2856
• Languages: English
• ISSNs: 0894-3370

Abstract

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.