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

[21] NEW EXACT SOLUTIONS OF CLASSICAL SINE-GORDON EQUATION IN 2+1 AND 3+1 DIMENSIONS [J].

LEIBBRANDT, G .

PHYSICAL REVIEW LETTERS, 1978, 41 (07) :435-438

[22] A least-squares preconditioner for radial basis functions collocation methods [J].

Ling, LV ;

Kansa, EJ .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2005, 23 (1-2) :31-54

[23] On the use of boundary conditions for variational formulations arising in financial mathematics [J].

Marcozzi, MD ;

Choi, S ;

Chen, CS .

APPLIED MATHEMATICS AND COMPUTATION, 2001, 124 (02) :197-214

[24] Combination of finite difference method and meshless method based on radial basis functions to solve fractional stochastic advection-diffusion equations [J].

Mirzaee, Farshid ;

Samadyar, Nasrin .

ENGINEERING WITH COMPUTERS, 2020, 36 (04) :1673-1686

[25] Numerical Solution of Time Fractional Stochastic Korteweg-de Vries Equation via Implicit Meshless Approach [J].

Mirzaee, Farshid ;

Samadyar, Nasrin .

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 2019, 43 (A6) :2905-2912

[26] On the numerical solution of fractional stochastic integro-differential equations via meshless discrete collocation method based on radial basis functions [J].

Mirzaee, Farshid ;

Samadyar, Nasrin .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2019, 100 :246-255

[27] Using radial basis functions to solve two dimensional linear stochastic integral equations on non-rectangular domains [J].

Mirzaee, Farshid ;

Samadyar, Nasrin .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2018, 92 :180-195

[28] A MODEL UNIFIELD FIELD EQUATION [J].

PERRING, JK ;

SKYRME, THR .

NUCLEAR PHYSICS, 1962, 31 (04) :550-+

[29] A numerical solution of the coupled sine-Gordon equation using the modified decomposition method [J].

Ray, S. Saha .

APPLIED MATHEMATICS AND COMPUTATION, 2006, 175 (02) :1046-1054

[30] Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme [J].

Sheng, Q ;

Khaliq, AQM ;

Voss, DA .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2005, 68 (04) :355-373

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