Crank-Nicolson-DQM based on cubic exponential B-splines for the approximation of nonlinear Sine-Gordon equation

In this paper, Crank-Nicolson differential quadrature method based on cubic exponential B-spline (CExpB-spline) functions is presented to approximate the 1D nonlinear hyperbolic Sine-Gordon equation (SGE). The time derivative is discretized by the usual forward difference scheme while the differenti...

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Autores principales:	A.H. Msmali, Mohammad Tamsir, Abdullah Ali H. Ahmadini
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Hyperbolic SGE DQM CExpB-spline functions Crank-Nicolson scheme ROC Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/457c10f0b628457281d89450a456668f
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id	oai:doaj.org-article:457c10f0b628457281d89450a456668f
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spelling	oai:doaj.org-article:457c10f0b628457281d89450a456668f2021-11-22T04:21:36ZCrank-Nicolson-DQM based on cubic exponential B-splines for the approximation of nonlinear Sine-Gordon equation2090-447910.1016/j.asej.2021.04.004https://doaj.org/article/457c10f0b628457281d89450a456668f2021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2090447921001672https://doaj.org/toc/2090-4479In this paper, Crank-Nicolson differential quadrature method based on cubic exponential B-spline (CExpB-spline) functions is presented to approximate the 1D nonlinear hyperbolic Sine-Gordon equation (SGE). The time derivative is discretized by the usual forward difference scheme while the differential quadrature method (DQM) is used to integrate the spatial derivatives. The discretization of the problem gives systems of linear equations. Three numerical examples are chosen to investigate the efficiency and accuracy of the method. It is observed that the proposed method provides excellent results than the existing methods. The rate of convergence (ROC) of the present method is obtained numerically showing that the method is second-order accurate in space.A.H. MsmaliMohammad TamsirAbdullah Ali H. AhmadiniElsevierarticleHyperbolic SGEDQMCExpB-spline functionsCrank-Nicolson schemeROCEngineering (General). Civil engineering (General)TA1-2040ENAin Shams Engineering Journal, Vol 12, Iss 4, Pp 4091-4097 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Hyperbolic SGE DQM CExpB-spline functions Crank-Nicolson scheme ROC Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Hyperbolic SGE DQM CExpB-spline functions Crank-Nicolson scheme ROC Engineering (General). Civil engineering (General) TA1-2040 A.H. Msmali Mohammad Tamsir Abdullah Ali H. Ahmadini Crank-Nicolson-DQM based on cubic exponential B-splines for the approximation of nonlinear Sine-Gordon equation
description	In this paper, Crank-Nicolson differential quadrature method based on cubic exponential B-spline (CExpB-spline) functions is presented to approximate the 1D nonlinear hyperbolic Sine-Gordon equation (SGE). The time derivative is discretized by the usual forward difference scheme while the differential quadrature method (DQM) is used to integrate the spatial derivatives. The discretization of the problem gives systems of linear equations. Three numerical examples are chosen to investigate the efficiency and accuracy of the method. It is observed that the proposed method provides excellent results than the existing methods. The rate of convergence (ROC) of the present method is obtained numerically showing that the method is second-order accurate in space.
format	article
author	A.H. Msmali Mohammad Tamsir Abdullah Ali H. Ahmadini
author_facet	A.H. Msmali Mohammad Tamsir Abdullah Ali H. Ahmadini
author_sort	A.H. Msmali
title	Crank-Nicolson-DQM based on cubic exponential B-splines for the approximation of nonlinear Sine-Gordon equation
title_short	Crank-Nicolson-DQM based on cubic exponential B-splines for the approximation of nonlinear Sine-Gordon equation
title_full	Crank-Nicolson-DQM based on cubic exponential B-splines for the approximation of nonlinear Sine-Gordon equation
title_fullStr	Crank-Nicolson-DQM based on cubic exponential B-splines for the approximation of nonlinear Sine-Gordon equation
title_full_unstemmed	Crank-Nicolson-DQM based on cubic exponential B-splines for the approximation of nonlinear Sine-Gordon equation
title_sort	crank-nicolson-dqm based on cubic exponential b-splines for the approximation of nonlinear sine-gordon equation
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/457c10f0b628457281d89450a456668f
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Crank-Nicolson-DQM based on cubic exponential B-splines for the approximation of nonlinear Sine-Gordon equation

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