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A numerical solution of the equal width wave equation by a lumped Galerkin method. (English) Zbl 1082.65574
Summary: The equal width wave equation is solved by a numerical technique based on a lumped Galerkin method using quadratic B-spline finite elements to investigate the motion of a single solitary wave, development of two solitary waves interaction and an undular bore. The obtained results are compared with published numerical solutions. A linear stability analysis of the method is also investigated.

65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
35L75Nonlinear hyperbolic PDE of higher $(>2)$ order
35Q51Soliton-like equations
65M12Stability and convergence of numerical methods (IVP of PDE)
Full Text: DOI
[1] Morrison, P. J.; Meiss, J. D.; Carey, J. R.: Scattering of RLW solitary waves. Physica D 11, 324-336 (1984) · Zbl 0599.76028
[2] Gardner, L. R. T.; Gardner, G. A.; Ayoub, F. A.; Amein, N. K.: Simulation of the EW undular bore. Commun. numer. Meth. eng. 13, 583-592 (1997) · Zbl 0883.76048
[3] Zaki, S. I.: A least-squares finite element scheme for the EW equation. Comput. meth. Appl. mech. Eng. 189, 587-594 (2000) · Zbl 0963.76057
[4] Zaki, S. I.: Solitary waves induced by the boundary forced EW equation. Comput. meth. Appl. mech. Eng. 190, 4881-4887 (2001) · Zbl 1011.76048
[5] Raslan, K. R.: A computational method for the equal width equation. Int. J. Comp. math. 81, 63-72 (2004) · Zbl 1047.65086
[6] A. Dogan, Application of Galerkin’s method to equal width wave equation, Appl. Math. Comput. (in press). · Zbl 1063.65104
[7] B. Saka, D. Irk, I. Dag, Numerical study of the equal width wave equation, Hadronic J. (in press). · Zbl 1087.65598
[8] Prenter, P. M.: Splines and variational methods. (1975) · Zbl 0344.65044
[9] Smith, G. D.: Numerical solution of partial differential equations: finite difference methods. (1987)
[10] Olver, P. J.: Euler operators and conservation laws of the BBM equation. Math. proc. Camb. phil. Soc. 85, 143-159 (1979) · Zbl 0387.35050