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Solving one‐dimensional nonlinear stochastic Sine‐Gordon equation with a new meshfree technique
Author(s) -
Mirzaee Farshid,
Rezaei Shadi,
Samadyar Nasrin
Publication year - 2020
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.2856
Subject(s) - mathematics , nonlinear system , radial basis function , sine , sine gordon equation , variable (mathematics) , gaussian , finite difference , work (physics) , mathematical analysis , finite difference method , boundary (topology) , computer science , geometry , soliton , physics , artificial neural network , quantum mechanics , machine learning , thermodynamics
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.