Collocation Method using Quartic B-Splines for Solving the Modified RLW Equation

Abdel Maksoud A  Soliman  nbsp

doi:10.17485/ijst/2017/v10i31/116266

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Collocation Method using Quartic B-Splines for Solving the Modified RLW Equation

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2017/v10i31/116266

Year: 2017, Volume: 10, Issue: 30, Pages: 1-7

Original Article

Collocation Method using Quartic B-Splines for Solving the Modified RLW Equation

Abdel-Maksoud A. Soliman^*

*Author for the correspondence:
Abdel-Maksoud A. Soliman
Department of Mathematics, College of Science & Arts, University of Bisha, Bisha – 61922, PO Box 344, Kingdom of Saudi Arabia; [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid knots points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.

Keywords: Collocation Method, MRLW Equation, Quartic B-splines, Solitons.