Approximation of the RLW equation by the least square cubic \(B\)-spline finite element method
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Publication:5950107
DOI10.1016/S0307-904X(00)00030-5zbMath0990.65110OpenAlexW2025241285MaRDI QIDQ5950107
Publication date: 23 August 2002
Published in: Applied Mathematical Modelling (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0307-904x(00)00030-5
numerical resultsevolution equationfinite element methodsregularized long wave equationPetrov-Galerkin methodleast squares methodcubic B-splinesquadratic nonlinearityThomas algorithm
Nonlinear parabolic equations (35K55) KdV equations (Korteweg-de Vries equations) (35Q53) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)
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Cites Work
- Unnamed Item
- A space-time least-square finite element scheme for advection-diffusion equations
- Petrov-Galerkin methods for nonlinear dispersive waves
- Numerical study of the regularized long-wave equation. I: Numerical methods
- Galerkin methods applied to some model equations for non-linear dispersive waves
- Numerical solutions of the regularized long-wave equation
- The Fourier pseudospectral method with a restrain operator for the RLW equation
- Least-squares quadratic B-spline finite element method for the regularised long wave equation
- Solitary waves of the regularised long-wave equation
- Numerical solution of regularized long-wave equation
- Euler operators and conservation laws of the BBM equation
- A B‐spline finite element method for the regularized long wave equation
- Model equations for long waves in nonlinear dispersive systems
- A least-squares finite element scheme for the RLW equation
- Conservative scheme for a model of nonlinear dispersive waves and its solitary waves induced by boundary motion