Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations

The KdV equation, which appears as an asymptotic model in physical systems ranging from water waves to plasma physics, has been studied. In this paper, we are concerned with dispersive nonlinear KdV equations by using two reliable methods: Shehu Adomian decomposition method (STADM) and the classical...

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Autores principales:	Appadu Appanah Rao, Kelil Abey Sherif
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	modified adomian decomposition method classical finite difference method nonlinear kdv equations blow up 35a25 35a22 34a45 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/83786f6978294ebbb129326a6c66911b
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spelling	oai:doaj.org-article:83786f6978294ebbb129326a6c66911b2021-12-05T14:10:45ZComparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations2391-466110.1515/dema-2021-0039https://doaj.org/article/83786f6978294ebbb129326a6c66911b2021-11-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0039https://doaj.org/toc/2391-4661The KdV equation, which appears as an asymptotic model in physical systems ranging from water waves to plasma physics, has been studied. In this paper, we are concerned with dispersive nonlinear KdV equations by using two reliable methods: Shehu Adomian decomposition method (STADM) and the classical finite difference method for solving three numerical experiments. STADM is constructed by combining Shehu’s transform and Adomian decomposition method, and the nonlinear terms can be easily handled using Adomian’s polynomials. The Shehu transform is used to accelerate the convergence of the solution series in most cases and to overcome the deficiency that is mainly caused by unsatisfied conditions in other analytical techniques. We compare the approximate and numerical results with the exact solution for the two numerical experiments. The third numerical experiment does not have an exact solution and we compare profiles from the two methods vs the space domain at some values of time. This study provides us with information about which of the two methods are effective based on the numerical experiment chosen. Knowledge acquired will enable us to construct methods for other related partial differential equations such as stochastic Korteweg-de Vries (KdV), KdV-Burgers, and fractional KdV equations.Appadu Appanah RaoKelil Abey SherifDe Gruyterarticlemodified adomian decomposition methodclassical finite difference methodnonlinear kdv equationsblow up35a2535a2234a45MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 377-409 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	modified adomian decomposition method classical finite difference method nonlinear kdv equations blow up 35a25 35a22 34a45 Mathematics QA1-939
spellingShingle	modified adomian decomposition method classical finite difference method nonlinear kdv equations blow up 35a25 35a22 34a45 Mathematics QA1-939 Appadu Appanah Rao Kelil Abey Sherif Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations
description	The KdV equation, which appears as an asymptotic model in physical systems ranging from water waves to plasma physics, has been studied. In this paper, we are concerned with dispersive nonlinear KdV equations by using two reliable methods: Shehu Adomian decomposition method (STADM) and the classical finite difference method for solving three numerical experiments. STADM is constructed by combining Shehu’s transform and Adomian decomposition method, and the nonlinear terms can be easily handled using Adomian’s polynomials. The Shehu transform is used to accelerate the convergence of the solution series in most cases and to overcome the deficiency that is mainly caused by unsatisfied conditions in other analytical techniques. We compare the approximate and numerical results with the exact solution for the two numerical experiments. The third numerical experiment does not have an exact solution and we compare profiles from the two methods vs the space domain at some values of time. This study provides us with information about which of the two methods are effective based on the numerical experiment chosen. Knowledge acquired will enable us to construct methods for other related partial differential equations such as stochastic Korteweg-de Vries (KdV), KdV-Burgers, and fractional KdV equations.
format	article
author	Appadu Appanah Rao Kelil Abey Sherif
author_facet	Appadu Appanah Rao Kelil Abey Sherif
author_sort	Appadu Appanah Rao
title	Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations
title_short	Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations
title_full	Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations
title_fullStr	Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations
title_full_unstemmed	Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations
title_sort	comparison of modified adm and classical finite difference method for some third-order and fifth-order kdv equations
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/83786f6978294ebbb129326a6c66911b
work_keys_str_mv	AT appaduappanahrao comparisonofmodifiedadmandclassicalfinitedifferencemethodforsomethirdorderandfifthorderkdvequations AT kelilabeysherif comparisonofmodifiedadmandclassicalfinitedifferencemethodforsomethirdorderandfifthorderkdvequations
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Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations

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