Application of Bernstein collocation method for solving the generalized regularized long wave equations

The regularized and the modified regularized long wave (RLW and MRLW) equations are solved numerically by the Bernstein polynomials in both the space and time directions based on Kronecker product. In this paper, we applied a fully different Bernstein collocation method than the other methods which...

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Autor principal:	D.A. Hammad
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Bernstein collocation method RLW equation MRLW equation Kronecker product Partial differential equations Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/24711848de684b0fa9b0dd3e26190452
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spelling	oai:doaj.org-article:24711848de684b0fa9b0dd3e261904522021-11-22T04:21:38ZApplication of Bernstein collocation method for solving the generalized regularized long wave equations2090-447910.1016/j.asej.2021.04.005https://doaj.org/article/24711848de684b0fa9b0dd3e261904522021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2090447921001702https://doaj.org/toc/2090-4479The regularized and the modified regularized long wave (RLW and MRLW) equations are solved numerically by the Bernstein polynomials in both the space and time directions based on Kronecker product. In this paper, we applied a fully different Bernstein collocation method than the other methods which used Bernstein polynomials to solve the problems. The approximate solution is defined by the Bernstein polynomials in all directions. A general form for any m derivative of any Bernstein polynomials is constructed. A general matrix form for the vector of any m derivative of any Bernstein polynomials is also constructed. Convergence study for the proposed numerical scheme is investigated. To determine the conservation properties of the RLW and MRLW equations, three invariants of motion (I1, I2 and I3) are computed. To test the accuracy, two error norms (‖E‖2 and ‖E‖∞) are evaluated. Numerical outcomes and comparisons with other techniques for the single and the interaction of two solitary waves for RLW and MRLW equations are presented.D.A. HammadElsevierarticleBernstein collocation methodRLW equationMRLW equationKronecker productPartial differential equationsEngineering (General). Civil engineering (General)TA1-2040ENAin Shams Engineering Journal, Vol 12, Iss 4, Pp 4081-4089 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Bernstein collocation method RLW equation MRLW equation Kronecker product Partial differential equations Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Bernstein collocation method RLW equation MRLW equation Kronecker product Partial differential equations Engineering (General). Civil engineering (General) TA1-2040 D.A. Hammad Application of Bernstein collocation method for solving the generalized regularized long wave equations
description	The regularized and the modified regularized long wave (RLW and MRLW) equations are solved numerically by the Bernstein polynomials in both the space and time directions based on Kronecker product. In this paper, we applied a fully different Bernstein collocation method than the other methods which used Bernstein polynomials to solve the problems. The approximate solution is defined by the Bernstein polynomials in all directions. A general form for any m derivative of any Bernstein polynomials is constructed. A general matrix form for the vector of any m derivative of any Bernstein polynomials is also constructed. Convergence study for the proposed numerical scheme is investigated. To determine the conservation properties of the RLW and MRLW equations, three invariants of motion (I1, I2 and I3) are computed. To test the accuracy, two error norms (‖E‖2 and ‖E‖∞) are evaluated. Numerical outcomes and comparisons with other techniques for the single and the interaction of two solitary waves for RLW and MRLW equations are presented.
format	article
author	D.A. Hammad
author_facet	D.A. Hammad
author_sort	D.A. Hammad
title	Application of Bernstein collocation method for solving the generalized regularized long wave equations
title_short	Application of Bernstein collocation method for solving the generalized regularized long wave equations
title_full	Application of Bernstein collocation method for solving the generalized regularized long wave equations
title_fullStr	Application of Bernstein collocation method for solving the generalized regularized long wave equations
title_full_unstemmed	Application of Bernstein collocation method for solving the generalized regularized long wave equations
title_sort	application of bernstein collocation method for solving the generalized regularized long wave equations
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/24711848de684b0fa9b0dd3e26190452
work_keys_str_mv	AT dahammad applicationofbernsteincollocationmethodforsolvingthegeneralizedregularizedlongwaveequations
_version_	1718418211251159040

Application of Bernstein collocation method for solving the generalized regularized long wave equations

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