Open Access Research

Numerical approximation to a solution of the modified regularized long wave equation using quintic B-splines

Seydi Battal Gazi Karakoc1, Nuri Murat Yagmurlu2* and Yusuf Ucar2

Author Affiliations

1 Department of Mathematics, Faculty of Science and Art, Nevsehir University, Nevsehir, 50300, Turkey

2 Department of Mathematics, Faculty of Science and Art, Inönü University, Malatya, 44280, Turkey

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Boundary Value Problems 2013, 2013:27  doi:10.1186/1687-2770-2013-27

Published: 14 February 2013

Abstract

In this work, a numerical solution of the modified regularized long wave (MRLW) equation is obtained by the method based on collocation of quintic B-splines over the finite elements. A linear stability analysis shows that the numerical scheme based on Von Neumann approximation theory is unconditionally stable. Test problems including the solitary wave motion, the interaction of two and three solitary waves and the Maxwellian initial condition are solved to validate the proposed method by calculating error norms <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/27/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/27/mathml/M1">View MathML</a> and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/27/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/27/mathml/M2">View MathML</a> that are found to be marginally accurate and efficient. The three invariants of the motion have been calculated to determine the conservation properties of the scheme. The obtained results are compared with other earlier results.

MSC: 97N40, 65N30, 65D07, 76B25, 74S05.

Keywords:
MRLW equation; collocation; finite element method; B-spline; solitary waves