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Application of a lumped Galerkin method to the regularized long wave equation. (English) Zbl 1090.65114
Summary: A lumped Galerkin method based on quadratic B-spline finite elements is used to find numerical solutions of the one-dimensional regularized long wave equation with a variant of initial and boundary conditions. The obtained numerical results show that the present method is a remarkably successful numerical technique for solving the equation. Results are compared with published numerical solutions. A linear stability analysis of the scheme is also investigated.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L75 Higher-order nonlinear hyperbolic equations
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