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Bhardwaj, D.; Shankar, R.

A computational method for regularized long wave equation. (English) Zbl 0965.65108

Comput. Math. Appl. 40, No. 12, 1397-1404 (2000).
Summary: Quintic spline technique and splitting method have been used to develop a new-finite difference method to solve regularized long wave equation. The convergence and the stability of the proposed method are discussed. Then, it is used to model solitary wave motion and undular bore development by solving two test examples.

Cited in 52 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)

Keywords:

numerical examples; operator splitting; undular bore; penta-diagonal matrix; solitons; Korteweg-de Vries equation; quintic spline; finite difference method; regularized long wave equation; convergence; stability
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\textit{D. Bhardwaj} and \textit{R. Shankar}, Comput. Math. Appl. 40, No. 12, 1397--1404 (2000; Zbl 0965.65108)
Full Text: DOI

References:

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[3] Eilbeck, J. C.; McGuire, G. R., Numerical study of regularized long wave equation; I: Numerical methods, J. Comput. Phys., 19, 43 (1975) · Zbl 0325.65054
[4] Bona, J. L.; Pyrant, P. J., A mathematical model for long wave generated by wave makers in nonlinear dispersive systems, (Proc. Cambridge Phil. Soc., 73 (1973)), 391 · Zbl 0261.76007
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