×

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.

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
35Q51 Soliton equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI

References:

[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), John-Wiley New York · Zbl 0344.65044
[9] Smith, G.D., Numerical solution of partial differential equations: finite difference methods, (1987), Clarendon Oxford
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.