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A lumped Galerkin method for the numerical solution of the modified equal-width wave equation using quadratic B-splines. (English) Zbl 1111.65086

Summary: The numerical solution of the one-dimensional modified equal width wave (MEW) equation is obtained by using a lumped Galerkin method based on quadratic B-spline finite elements. The motion of a single solitary wave and the interaction of two solitary waves are studied. The numerical results obtained show that the present method is a remarkably successful numerical technique for solving the MEW equation. A linear stability analysis of the scheme is also investigated.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L75 Higher-order nonlinear hyperbolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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[1] DOI: 10.1016/0167-2789(84)90014-9 · Zbl 0599.76028
[2] DOI: 10.1016/S0010-4655(99)00471-3 · Zbl 0951.65098
[3] Hamdi, S., Enright, W. H., Schiesser, W. E. and Gottlieb, J. J. Exact solutions of the generalized equal width wave equation. Proceedings of the International Conference on Computational Science and its Applications, pp.725–734. Berlin: Springer-Verlag. LNCS 2668
[4] DOI: 10.1080/0020716042000272539 · Zbl 1064.65114
[5] DOI: 10.1016/j.cnsns.2004.07.001 · Zbl 1078.35108
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[8] DOI: 10.1016/j.cam.2005.04.026 · Zbl 1086.65094
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