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COLLOCATION METHOD USING QUARTIC B-SPLINE FOR NUMERICAL SOLUTION OF THE MODIFIED EQUAL WIDTH WAVE EQUATION  

Islam, Siraj-Ul (Department of Basic Sciences, NWFP University of Engineering and Technology)
Haq, Fazal-I (Department of Maths, Stats and Computer Science, NWFP Agricultural University)
Tirmizi, Ikram A. (Faculty of Engineering Sciences, GIK Institute of Engineering Sciences)
Publication Information
Journal of applied mathematics & informatics / v.28, no.3_4, 2010 , pp. 611-624 More about this Journal
Abstract
A Numerical scheme based on collocation method using quartic B-spline functions is designed for the numerical solution of one-dimensional modified equal width wave (MEW) wave equation. Using Von-Neumann approach the scheme is shown to be unconditionally stable. Performance of the method is validated through test problems including single wave, interaction of two waves and use of Maxwellian initial condition. Using error norms $L_2$ and $L_{\infty}$ and conservative properties of mass, momentum and energy, accuracy and efficiency of the suggested method is established through comparison with the existing numerical techniques.
Keywords
Modified equal width wave (MEW) equation; B-spline collocation method; nonlinear partial differential equations; stability analysis;
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