Efficiency of high-order accurate difference schemes for the Korteweg-de Vries equation

DOI10.1155/2014/862403zbMath1407.65124OpenAlexW2137849157WikidataQ59070181 ScholiaQ59070181MaRDI QIDQ1719267

Kanyuta Poochinapan, Ben Wongsaijai, Thongchai Disyadej

Publication date: 8 February 2019

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2014/862403

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items

Convergence analysis of the higher-order global mass-preserving numerical method for the symmetric regularized long-wave equation, On solitary wave solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara equations with the dual-power law nonlinearities, Evaluation of shallow water waves modelled by the Rosenau-Kawahara equation using pseudo-compact finite difference approach, A novel convenient finite difference method for shallow water waves derived by fifth‐order Kortweg and De‐Vries‐type equation, Analytical and numerical studies on dynamic of complexiton solution for complex nonlinear dispersive model, Performance of compact and non-compact structure preserving algorithms to traveling wave solutions modeled by the Kawahara equation, Unnamed Item, On the identification of nonlinear terms in the generalized Camassa-Holm equation involving dual-power law nonlinearities, Optimal decay rates of the dissipative shallow water waves modeled by coupling the rosenau-RLW equation and the rosenau-Burgers equation with power of nonlinearity, Compact structure-preserving algorithm with high accuracy extended to the improved Boussinesq equation, Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation, Novel algorithm based on modification of Galerkin finite element method to general Rosenau-RLW equation in (2 + 1)-dimensions, High-performance computing of structure-preserving algorithm for the coupled BBM system formulated by weighted compact difference operators

Cites Work

• Single and multidomain Chebyshev collocation methods for the Korteweg-de Vries equation
• Alternating segment explicit-implicit scheme for nonlinear third-order KdV equation
• Exact solutions and conservation laws for coupled generalized Korteweg-de Vries and quintic regularized long wave equations
• Simulations of solitons using quadratic spline finite elements
• Approximations of the KdV equation by least squares finite elements
• Galerkin methods applied to some model equations for non-linear dispersive waves
• Spectral approximation of third-order problems
• A Legendre--Petrov--Galerkin and Chebyshev Collocation Method for Third-Order Differential Equations
• On Stability of Some Finite Difference Schemes for the Korteweg-de Vries Equation
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• On the rate of convergence of a collocation projection of the KdV equation
• Error analysis for spectral approximation of the Korteweg-de Vries equation
• A New Dual-Petrov-Galerkin Method for Third and Higher Odd-Order Differential Equations: Application to the KDV Equation
• Collocation solution of the Korteweg–de Vries equation using septic splines
• A scheme with a higher-order discrete invariant for the KdV equation
• A nonlinear Galerkin method for the shallow-water equations on periodic domains