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

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)
Full Text: DOI
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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
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[5] Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L., The theory of splines and their applications, (1967), Academic Press London · Zbl 0158.15901
[6] Richtmyer, R.D.; Morton, K.W., Difference methods for initial value problems, (1967), Interscience New York · Zbl 0155.47502
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