An adaptive method of lines solution of the Korteweg-de Vries equation

DOI10.1016/S0898-1221(98)00093-5zbMath0999.65098WikidataQ127436281 ScholiaQ127436281MaRDI QIDQ1608426

W. E. Schiesser, Philippe Saucez, Alain Vande Wouwer

Publication date: 6 August 2002

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

comparison of methodscomputational experimentsmethod of linesfinite difference schemesKorteweg-de Vries equationremeshing algorithm

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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items

Application of the optimal homotopy asymptotic method for the solution of the Korteweg-de Vries equation ⋮ An MEBDF package for the numerical solution of large sparse systems of stiff initial value problems ⋮ A grid redistribution method for singular problems ⋮ Adaptive method of lines solutions for the extended fifth-order Korteweg-de Vries equation ⋮ An application for a modified KdV equation by the decomposition method and finite element method ⋮ Comparison of the solutions obtained by B-spline FEM and ADM of KdV equation ⋮ An application for a generalized KdV equation by the decomposition method

Uses Software

• RODAS
• MOVCOL
• Algorithm 731
• CWRESU
• CWRESX

Cites Work

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• A Hermite rational approximation method for the Korteweg-de Vries equation
• Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation
• A method for the integration in time of certain partial differential equations
• A simple adaptive technique for nonlinear wave problems
• Method of lines solution of the Korteweg-de Vries equation
• Some user-oriented comparisons of adaptive grid methods for partial differential equations in one space dimension
• Some observations on a static spatial remeshing method based on equidistribution principles
• A moving collocation method for solving time dependent partial differential equations
• Generation of Finite Difference Formulas on Arbitrarily Spaced Grids
• Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations

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