Regarding the group preserving scheme and method of line to the numerical simulations of Klein–Gordon model

In this work a powerful method is presented to solve the Klein–Gordon equation (KGE). Firstly, a discretization is implemented on the original equation. Then a geometric technique is applied to obtain the approximate solutions. Some examples containing one-dimensional and two-dimensional are solved...

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Main Authors:	Wei Gao, Mohammad Partohaghighi, Haci Mehmet Baskonus, Samaneh Ghavi
Format:	Article
Language:	English
Published:	Elsevier 2019-12-01
Series:	Results in Physics
Online Access:	http://www.sciencedirect.com/science/article/pii/S2211379719319254

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spelling	doaj-8175cae1ee174250b06505de96ab64ca2020-11-24T21:17:51ZengElsevierResults in Physics2211-37972019-12-0115Regarding the group preserving scheme and method of line to the numerical simulations of Klein–Gordon modelWei Gao0Mohammad Partohaghighi1Haci Mehmet Baskonus2Samaneh Ghavi3School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China; Corresponding author.Department of Mathematics, University of Bonab, Bonab, IranFaculty of Education, Department of Mathematics and Science Education, Harran University, Sanliurfa, TurkeyDepartment of Mathematics, University of Hakim Sabzevari, Sabzevar, IranIn this work a powerful method is presented to solve the Klein–Gordon equation (KGE). Firstly, a discretization is implemented on the original equation. Then a geometric technique is applied to obtain the approximate solutions. Some examples containing one-dimensional and two-dimensional are solved to prove the power and the capability of the offered scheme. Indeed, graphs of the exact solution, numerical solution, absolute error and the contour plot of error are provided successfully. Keywords: Method of line, Nonlinear Klein–Gordon equation, Group preserving schemehttp://www.sciencedirect.com/science/article/pii/S2211379719319254
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Wei Gao Mohammad Partohaghighi Haci Mehmet Baskonus Samaneh Ghavi
spellingShingle	Wei Gao Mohammad Partohaghighi Haci Mehmet Baskonus Samaneh Ghavi Regarding the group preserving scheme and method of line to the numerical simulations of Klein–Gordon model Results in Physics
author_facet	Wei Gao Mohammad Partohaghighi Haci Mehmet Baskonus Samaneh Ghavi
author_sort	Wei Gao
title	Regarding the group preserving scheme and method of line to the numerical simulations of Klein–Gordon model
title_short	Regarding the group preserving scheme and method of line to the numerical simulations of Klein–Gordon model
title_full	Regarding the group preserving scheme and method of line to the numerical simulations of Klein–Gordon model
title_fullStr	Regarding the group preserving scheme and method of line to the numerical simulations of Klein–Gordon model
title_full_unstemmed	Regarding the group preserving scheme and method of line to the numerical simulations of Klein–Gordon model
title_sort	regarding the group preserving scheme and method of line to the numerical simulations of klein–gordon model
publisher	Elsevier
series	Results in Physics
issn	2211-3797
publishDate	2019-12-01
description	In this work a powerful method is presented to solve the Klein–Gordon equation (KGE). Firstly, a discretization is implemented on the original equation. Then a geometric technique is applied to obtain the approximate solutions. Some examples containing one-dimensional and two-dimensional are solved to prove the power and the capability of the offered scheme. Indeed, graphs of the exact solution, numerical solution, absolute error and the contour plot of error are provided successfully. Keywords: Method of line, Nonlinear Klein–Gordon equation, Group preserving scheme
url	http://www.sciencedirect.com/science/article/pii/S2211379719319254
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Regarding the group preserving scheme and method of line to the numerical simulations of Klein–Gordon model

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