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A finite element method for equal width equation. (English) Zbl 1088.65084
Summary: A numerical solution of the equal width (EW) equation is obtained using the space-splitting technique and the quadratic B-spline Galerkin finite element method. Solitary wave motion, interaction of two solitary waves, wave undulation and wave generation are studied using the proposed method. Comparisons are made with analytical solutions and with some spline finite element method calculations at selected times. Accuracy and efficiency are discussed by computing the numerical conserved laws and \(L_{2}, L_{\infty}\) error norms.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L75 Higher-order nonlinear hyperbolic equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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