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Solitary waves of the regularised long-wave equation. (English) Zbl 0717.65072
Authors’ summary: A finite element solution of the regularized long wave equation, based on Galerkin’s method using cubic splines as element shape functions, is set up. A linear stability analysis shows the scheme to be unconditionally stable. Test problems, including the migration and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evolution of a Maxwellian initial pulse is then studied.
Reviewer: W.Ames

65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
35L70Nonlinear second-order hyperbolic equations
Full Text: DOI
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