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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Bibliographic Details
Published in:Numerical methods for partial differential equations Vol. 37; no. 1; pp. 690 - 706
Main Authors: Başhan, Ali, Yağmurlu, N. Murat, Uçar, Yusuf, Esen, Alaattin
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.01.2021
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Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0749-159X
1098-2426
DOI:10.1002/num.22547