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

被引：39

作者：

Mirzaee, Farshid ^{[1
]}

Rezaei, Shadi ^{[1
]}

Samadyar, Nasrin ^{[1
]}

机构：

[1] Malayer Univ, Fac Math Sci & Stat, POB 65719-95863, Malayer, Iran

来源：

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING-ELECTRONIC NETWORKS DEVICES AND FIELDS | 2021年 / 34卷 / 04期

关键词：

Brownian motion process; one-dimensional stochastic Sine-Gordon equation; radial basis function; stochastic partial differential equations; DATA APPROXIMATION SCHEME; RADIAL BASIS FUNCTIONS; NUMERICAL-SOLUTION; KLEIN-GORDON; COLLOCATION; MULTIQUADRICS; SIMULATION; SOLITONS;

D O I：

10.1002/jnm.2856

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

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.

引用

页数：13

共 34 条

[1]

[Anonymous], 2005, CAMBRIDGE MONOGRAPHS

[2] FINITE-ELEMENT APPROXIMATION TO 2-DIMENSIONAL SINE-GORDON SOLITONS [J].

ARGYRIS, J ;

HAASE, M ;

HEINRICH, JC .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1991, 86 (01) :1-26

[3] Numerical solution of sine-Gordon equation by variational iteration method [J].

Batiha, B. ;

Noorani, M. S. M. ;

Hashim, I. .

PHYSICS LETTERS A, 2007, 370 (5-6) :437-440

[4] The solution of the two-dimensional sine-Gordon equation using the method of lines [J].

Bratsos, A. G. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 206 (01) :251-277

[5]

Bratsos AG., 2005, Appl. Numer. Anal. Comput. Math, V2, P189, DOI 10.1002/anac.200410035

[6] Finite element methods for semilinear elliptic stochastic partial differential equations [J].

Cao, Yanzhao ;

Yang, Hongtao ;

Yin, Li .

NUMERISCHE MATHEMATIK, 2007, 106 (02) :181-198

[7] Application of homotopy-perturbation method to Klein-Gordon and sine-Gordon equations [J].

Chowdhury, M. S. H. ;

Hashim, I. .

CHAOS SOLITONS & FRACTALS, 2009, 39 (04) :1928-1935

[8] Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions [J].

Dehghan, Mehdi ;

Shokri, Ali .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 230 (02) :400-410

[9] Meshless Local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity [J].

Dehghan, Mehdi ;

Mirzaei, Davoud .

APPLIED NUMERICAL MATHEMATICS, 2009, 59 (05) :1043-1058

[10] A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions [J].

Dehghan, Mehdi ;

Shokri, Ali .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2008, 79 (03) :700-715

← 1 2 3 4 →