A numerical solution of the modified regularized long wave equation using quartic B-splines

A numerical solution of the modified regularized long wave equation using quartic B-splines

In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained by subdomain finite element method using quartic B-spline functions. Solitary wave motion, interaction of two and three solitary waves and the development of the Maxwellian initial condition into so...

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Veröffentlicht in:TWMS journal of applied and engineering mathematics 2013-07, Vol.3 (2), p.231-244
Hauptverfasser: Karakoc, S. Battal Gazi, Geyikli, Turabi, Bashan, Ali
Format: Artikel
Sprache:eng
Schlagworte:
Computational efficiency
Computing time
Finite element analysis
Finite element method
Fluid mechanics
Initial conditions
Mathematical analysis
Mathematical models
Mathematical research
Norms
Solitary waves
Spline theory
Wave equation
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Zusammenfassung:In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained by subdomain finite element method using quartic B-spline functions. Solitary wave motion, interaction of two and three solitary waves and the development of the Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracy and efficiency of the proposed method are tested by calculating the numerical conserved laws and error norms [L.sub.2] and [L.sub.∞]. The obtained results show that the method is an effective numerical scheme to solve the MRLW equation. In addition, a linear stability analysis of the scheme is found to be unconditionally stable. Keywords: MRLW equation, Finite element method, Subdomain, Quartic B-Splines, Solitary waves. AMS Subject Classification: 97N40, 65N30, 65D07, 76B25, 74S05,74J35
ISSN:2146-1147
2146-1147