Single and multidomain Chebyshev collocation methods for the Korteweg-de Vries equation

DOI10.1007/BF02575839zbMath0689.65075MaRDI QIDQ582028

Donatella Pavoni

Publication date: 1988

Published in: Calcolo (Search for Journal in Brave)

zbMATH Keywords

numerical experimentsKorteweg-de Vries equationChebyshev polynomial expansionsChebyshev collocation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Partial differential equations of mathematical physics and other areas of application (35Q99) Applications to the sciences (65Z05)

Related Items (12)

Numerical study of the generalized Korteweg-de Vries equations with oscillating nonlinearities and boundary conditions ⋮ Stability of Spectral Collocation Schemes with Explicit-Implicit-Null Time-Marching for ConvectionDiffusion and Convection-Dispersion Equations ⋮ Multidomain pseudospectral methods for nonlinear convection-diffusion equations ⋮ Error estimates of a space-time Legendre spectral method for solving the Korteweg-de Vries equation ⋮ A multi-interval Chebyshev collocation approach for the stability of periodic delay systems with discontinuities ⋮ Efficiency of high-order accurate difference schemes for the Korteweg-de Vries equation ⋮ Unnamed Item ⋮ A Jacobi dual-Petrov Galerkin-Jacobi collocation method for solving Korteweg-de Vries equations ⋮ Novel algorithm based on modification of Galerkin finite element method to general Rosenau-RLW equation in (2 + 1)-dimensions ⋮ A boundary value problem for the KdV equation: comparison of finite-difference and Chebyshev methods ⋮ Numerical solutions of Korteweg-de Vries and Korteweg-de Vries-Burger's equations in a Bernstein polynomial basis ⋮ Truncation versus mapping in the spectral approximation to the Korteweg- de Vries equation

Cites Work

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• Spectral approximation of the periodic nonperiodic Navier-Stokes equations
• Fourier Methods with Extended Stability Intervals for the Korteweg–de Vries Equation
• Fourier Spectral Methods for Pseudoparabolic Equations
• Error analysis for spectral approximation of the Korteweg-de Vries equation
• An Iterative Procedure with Interface Relaxation for Domain Decomposition Methods
• The initial-value problem for the Korteweg-de Vries equation
• The Korteweg–deVries Equation: A Survey of Results
• Boundary Conditions in Chebyshev and Legendre Methods

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