A stable time–space Jacobi pseudospectral method for two-dimensional sine-Gordon equation

Mittal, A. K.

doi:10.1007/s12190-020-01316-9

Cited by 17 publications

(8 citation statements)

References 40 publications

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“…One of them is the balance between the dispersion and nonlinearity [1,2]. One of these models is SGE, which is a nonlinear partial differential equation with a nonlinear sine source term and its solution has the soliton like structure [3]. This equation has great importance in physical phenomena and some important applications include numerical forecasting, optical fibres, nonlinear optics, quantum field theory, etc.…”

Section: Introductionmentioning

confidence: 99%

Application of DRBEM for 2D sine-Gordon equation

Alsoy-Akgün

2021

Journal of Taibah University for Science

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This research paper introduces an application of dual reciprocity boundary element method (DRBEM) for the solution of sine-Gordon equation (SGE) in two-space dimension. Initially, the time derivatives are expanded using central difference schemes. After inserting the finite difference approximations into the governing equation, the pattern of the modified Helmholtz equation is obtained. The fundamental solution of modified Helmholtz equation is employed in the integral equation formulation. The inhomogeneous terms of the equation cause a domain integral in the integral equation formulation which leads to loss of advantage of the method. The DRBEM provides to transform the domain integral into the boundary integral by approximating the inhomogeneous term of the equation with thin plate spline (r 2 ln r). First, code validation of the procedure is done using a test problem and then proposed method is applied for several cases involving line and ring solitons to display its capacity to treat the problem. Presented numerical results are observed to be in good agreement with other numerical results available in the literature.

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Section: Introductionmentioning

confidence: 99%

Application of DRBEM for 2D sine-Gordon equation

Alsoy-Akgün

2021

Journal of Taibah University for Science

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“…There are some authors, who have applied spectral method for numerical solutions of various nonlinear partial differential equations [38–43]. In this paper, we propose a highly accurate Chebyshev pseudospectral method using orthogonal basis functions for numerical solutions of CMKdV equation, in both time and spatial direction.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions and stability analysis for solitary waves of complex modified Korteweg–de Vries equation using Chebyshev pseudospectral methods

Mittal

Balyan

2020

Numerical Methods Partial

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“…24 Besides, the pseudospectral method is also an emphatic and alternate numerical scheme for solving a wide range of linear and nonlinear fractional partial differential equations. [25][26][27][28][29][30] Lin and Xu 26 and Mohebbi 31 have used spectral method for the solution and stability analysis of time fractional nonlinear equations. They applied spectral method for space only, and finite difference scheme was used for time.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of time and space fractional coupled Burgers equations using time–space Chebyshev pseudospectral method

Mittal

Balyan

2020

Math Methods in App Sciences

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The aim of the paper is to develop and analyze a spectrally accurate time–space pseudospectral method to the approximate solution of nonlinear time and space fractional coupled Burgers equations. Liouville–Caputo fractional derivative formula is used to evaluate the fractional derivatives matrix at CGL points. Using the Chebyshev fractional derivative matrices, the given problem is reduced to a system of nonlinear algebraic equations. A mapping is used to transform the nonhomogeneous initial–boundary values to homogeneous initial–boundary values. Error analysis of the proposed method for the equation is presented. A model example of fractional coupled Burgers equations is tested for a set of fractional‐order derivatives. For the proposed method, highly accurate numerical results are obtained, which confirm the accuracy and efficiency of the proposed method.

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A stable time–space Jacobi pseudospectral method for two-dimensional sine-Gordon equation

Cited by 17 publications

References 40 publications

Application of DRBEM for 2D sine-Gordon equation

Application of DRBEM for 2D sine-Gordon equation

Numerical solutions and stability analysis for solitary waves of complex modified Korteweg–de Vries equation using Chebyshev pseudospectral methods

Numerical solutions of time and space fractional coupled Burgers equations using time–space Chebyshev pseudospectral method

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