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.


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
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