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Farshid Mirzaee

Farshid Mirzaee

Academic rank: Professor
ORCID: 0000-0002-1429-2548
Education: PhD.
ScopusId: 6508385954
HIndex: 34/00
Faculty: Mathematical Sciences and Statistics
Address: Faculty of Mathematical Sciences and Statistics, Department of Applied Mathematics, Malayer University, 4 Km Malayer-Arak Road, P. O. Box 65719-95863, Malayer, Iran.
Phone: +98 - 81 - 32457459

Research

Title
Solving one-dimensional nonlinear stochastic Sine-Gordon equation with a new meshfree technique
Type
JournalPaper
Keywords
Brownian motion process, One-dimensional stochastic Sine-Gordon equation, Radial basis function, Stochastic partial differential equations
Year
2021
Journal INTERNATIONAL JOURNAL OF NUMERICAL MODELLING-ELECTRONIC NETWORKS DEVICES AND FIELDS
DOI
Researchers Farshid Mirzaee

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.