Galerkin method for the numerical solution of the RLW equation using quadratic B-splines. (English) Zbl 1060.65109
Summary: A numerical solution of the regularised long wave (RLW) equation is obtained using space-splitting technique and quadratic B-spline Galerkin finite element method. Solitary wave motion, interaction of two solitary waves 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 \(L_2\), \(L_\infty\) 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 |
Keywords:
numerical examples; solitary waves; regularised long wave equation; B-spline Galerkin finite element methodReferences:
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