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Solitary waves of the splitted RLW equation. (English) Zbl 0984.65103

Summary: A combination of the splitting method and the cubic B-spline finite elements is used to solve the nonlinear regularized long wave (RLW) equation. This approach involves a Bubnov-Galerkin method with cubic B-spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solution region. Time integration of the resulting systems is effected using a Crank-Nicolson approximation. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent splitting difference scheme based on cubic spline interpolation functions, for different amplitudes ranging from a very small \((\geq 0.03)\) to a considerably high amplitudes \((\leq 0.3)\). The development of an undular bore is modeled.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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