Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation

The aim of this study is to improve the numerical solution of the modified equal width wave equation. For this purpose, finite difference method combined with differential quadrature method with Rubin and Graves linearizing technique has been used. Modified cubic B‐spline base functions are used as...

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Vydáno v:	Numerical methods for partial differential equations Ročník 37; číslo 1; s. 690 - 706
Hlavní autoři:	Başhan, Ali, Yağmurlu, N. Murat, Uçar, Yusuf, Esen, Alaattin
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Hoboken, USA John Wiley & Sons, Inc 01.01.2021 Wiley Subscription Services, Inc
Témata:	Algorithms B‐splines Differential equations differential quadrature method Exact solutions Finite difference method modified equal width equation Norms Numerical analysis Numerical methods Quadratures solitary wave Solitary waves Wave equations
ISSN:	0749-159X, 1098-2426
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Abstract	The aim of this study is to improve the numerical solution of the modified equal width wave equation. For this purpose, finite difference method combined with differential quadrature method with Rubin and Graves linearizing technique has been used. Modified cubic B‐spline base functions are used as base function. By the combination of two numerical methods and effective linearizing technique high accurate numerical algorithm is obtained. Three main test problems are solved for various values of the coefficients. To observe the performance of the present method, the error norms of the single soliton problem which has analytical solution are calculated. Besides these error norms, three invariants are reported. Comparison of the results displays that our algorithm produces superior results than those given in the literature.
AbstractList	The aim of this study is to improve the numerical solution of the modified equal width wave equation. For this purpose, finite difference method combined with differential quadrature method with Rubin and Graves linearizing technique has been used. Modified cubic B‐spline base functions are used as base function. By the combination of two numerical methods and effective linearizing technique high accurate numerical algorithm is obtained. Three main test problems are solved for various values of the coefficients. To observe the performance of the present method, the error norms of the single soliton problem which has analytical solution are calculated. Besides these error norms, three invariants are reported. Comparison of the results displays that our algorithm produces superior results than those given in the literature.
Author	Başhan, Ali Yağmurlu, N. Murat Uçar, Yusuf Esen, Alaattin
Author_xml	– sequence: 1 givenname: Ali orcidid: 0000-0001-8500-493X surname: Başhan fullname: Başhan, Ali email: alibashan@gmail.com organization: Zonguldak Bulent Ecevit University – sequence: 2 givenname: N. Murat orcidid: 0000-0003-1593-0254 surname: Yağmurlu fullname: Yağmurlu, N. Murat organization: Inonu University – sequence: 3 givenname: Yusuf orcidid: 0000-0003-1469-5002 surname: Uçar fullname: Uçar, Yusuf organization: Inonu University – sequence: 4 givenname: Alaattin orcidid: 0000-0002-7927-5941 surname: Esen fullname: Esen, Alaattin organization: Inonu University
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SubjectTerms	Algorithms B‐splines Differential equations differential quadrature method Exact solutions Finite difference method modified equal width equation Norms Numerical analysis Numerical methods Quadratures solitary wave Solitary waves Wave equations
Title	Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation
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