A Numerical Method for the Generalized Regularized Long Wave Equation Using a Reproducing Kernel Function

DOI10.1137/070683623zbMath1181.65125OpenAlexW1981139808MaRDI QIDQ3398247

Gyungsoo Woo, Seokchan Kim, Shu-Sen Xie, Su-Cheol Yi

Publication date: 28 September 2009

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/070683623

zbMATH Keywords

convergenceGalerkin methodnumerical resultsfinite elementssolitary wavesgeneralized regularized long wave equationreproducing kernel functionfully discrete approximationsemidiscretizations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Higher-order nonlinear hyperbolic equations (35L75) Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs (65M80)

Related Items (5)

Solitary wave solutions of the nonlinear generalized Pochhammer-Chree and regularized long wave equations ⋮ On the accuracy of some explicit and implicit methods for the inviscid GRLW equation subject to initial Gaussian conditions ⋮ A new energy conservative scheme for regularized long wave equation. ⋮ Numerical solution of GRLW equation using sinc-collocation method ⋮ On the convergence of difference schemes for generalized Benjamin–Bona–Mahony equation

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