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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.
MSC:
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)