A new technique for numerical solution of 1D and 2D non-linear coupled Burgers’ equations by using cubic Uniform Algebraic Trigonometric (UAT) tension B-spline based differential quadrature method

In present paper, a new technique is developed named Uniform Algebraic Trigonometric (UAT) tension B-spline based DQM, for the better numerical approximation of coupled 1D and coupled 2D Burgers’ equation. The formula of UAT tension B-spline of order 4 is developed in this paper, by using above-ment...

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Autores principales:	Mamta Kapoor, Varun Joshi
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Differential quadrature method Coupled 1D and coupled 2D Burgers’ equation Uniform Algebraic Trigonometric (UAT) tension B-spline Strong stability preserving Runge-Kutta – 43 method Error norms Matrix stability analysis method. Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/f2359e60a3324e398a611e107805ed41
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spelling	oai:doaj.org-article:f2359e60a3324e398a611e107805ed412021-11-22T04:20:58ZA new technique for numerical solution of 1D and 2D non-linear coupled Burgers’ equations by using cubic Uniform Algebraic Trigonometric (UAT) tension B-spline based differential quadrature method2090-447910.1016/j.asej.2020.11.030https://doaj.org/article/f2359e60a3324e398a611e107805ed412021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S209044792100143Xhttps://doaj.org/toc/2090-4479In present paper, a new technique is developed named Uniform Algebraic Trigonometric (UAT) tension B-spline based DQM, for the better numerical approximation of coupled 1D and coupled 2D Burgers’ equation. The formula of UAT tension B-spline of order 4 is developed in this paper, by using above-mentioned basis function. Strong stability preserving SSP-RK 43 method is implemented to solve obtained ordinary differential equations. To check the effectiveness and accuracy of the proposed scheme, L2 and L∞error norms are used. Four numerical experiments are discussed to put light upon applicability of scheme. By means of tables and figures, results obtained are given. Obtained results are in a good agreement with existing ones. Stability of proposed scheme is also checked by implementing the Matrix stability analysis method. This novel scheme will surely open some new dimensions in the field of numerical approximation, for other researchers in their future work.Mamta KapoorVarun JoshiElsevierarticleDifferential quadrature methodCoupled 1D and coupled 2D Burgers’ equationUniform Algebraic Trigonometric (UAT) tension B-splineStrong stability preserving Runge-Kutta – 43 methodError normsMatrix stability analysis method.Engineering (General). Civil engineering (General)TA1-2040ENAin Shams Engineering Journal, Vol 12, Iss 4, Pp 3947-3965 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Differential quadrature method Coupled 1D and coupled 2D Burgers’ equation Uniform Algebraic Trigonometric (UAT) tension B-spline Strong stability preserving Runge-Kutta – 43 method Error norms Matrix stability analysis method. Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Differential quadrature method Coupled 1D and coupled 2D Burgers’ equation Uniform Algebraic Trigonometric (UAT) tension B-spline Strong stability preserving Runge-Kutta – 43 method Error norms Matrix stability analysis method. Engineering (General). Civil engineering (General) TA1-2040 Mamta Kapoor Varun Joshi A new technique for numerical solution of 1D and 2D non-linear coupled Burgers’ equations by using cubic Uniform Algebraic Trigonometric (UAT) tension B-spline based differential quadrature method
description	In present paper, a new technique is developed named Uniform Algebraic Trigonometric (UAT) tension B-spline based DQM, for the better numerical approximation of coupled 1D and coupled 2D Burgers’ equation. The formula of UAT tension B-spline of order 4 is developed in this paper, by using above-mentioned basis function. Strong stability preserving SSP-RK 43 method is implemented to solve obtained ordinary differential equations. To check the effectiveness and accuracy of the proposed scheme, L2 and L∞error norms are used. Four numerical experiments are discussed to put light upon applicability of scheme. By means of tables and figures, results obtained are given. Obtained results are in a good agreement with existing ones. Stability of proposed scheme is also checked by implementing the Matrix stability analysis method. This novel scheme will surely open some new dimensions in the field of numerical approximation, for other researchers in their future work.
format	article
author	Mamta Kapoor Varun Joshi
author_facet	Mamta Kapoor Varun Joshi
author_sort	Mamta Kapoor
title	A new technique for numerical solution of 1D and 2D non-linear coupled Burgers’ equations by using cubic Uniform Algebraic Trigonometric (UAT) tension B-spline based differential quadrature method
title_short	A new technique for numerical solution of 1D and 2D non-linear coupled Burgers’ equations by using cubic Uniform Algebraic Trigonometric (UAT) tension B-spline based differential quadrature method
title_full	A new technique for numerical solution of 1D and 2D non-linear coupled Burgers’ equations by using cubic Uniform Algebraic Trigonometric (UAT) tension B-spline based differential quadrature method
title_fullStr	A new technique for numerical solution of 1D and 2D non-linear coupled Burgers’ equations by using cubic Uniform Algebraic Trigonometric (UAT) tension B-spline based differential quadrature method
title_full_unstemmed	A new technique for numerical solution of 1D and 2D non-linear coupled Burgers’ equations by using cubic Uniform Algebraic Trigonometric (UAT) tension B-spline based differential quadrature method
title_sort	new technique for numerical solution of 1d and 2d non-linear coupled burgers’ equations by using cubic uniform algebraic trigonometric (uat) tension b-spline based differential quadrature method
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/f2359e60a3324e398a611e107805ed41
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A new technique for numerical solution of 1D and 2D non-linear coupled Burgers’ equations by using cubic Uniform Algebraic Trigonometric (UAT) tension B-spline based differential quadrature method

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