Convergence of a finite difference method for the KdV and modified KdV equations with \(L^2\) data

DOI10.4171/PM/1924zbMath1298.65120arXiv1202.1232MaRDI QIDQ360093

Paulo Amorim, M. S. Figueira

Publication date: 26 August 2013

Published in: Portugaliae Mathematica. Nova Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.1232

zbMATH Keywords

convergencestabilizationnumerical experimentKorteweg-de Vries equation, finite difference method

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) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items

Convergence of a semi-discrete numerical method for a class of nonlocal nonlinear wave equations, The linear stability of shock waves for the nonlinear Schrödinger-inviscid Burgers system, Convergence of a full discrete finite element method for the Korteweg-de Vries equation, Numerical analysis of a new conservative scheme for the 2D generalized Rosenau-RLW equation, Convergence of the Crank-Nicolson extrapolation scheme for the Korteweg-de Vries equation

Cites Work

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• Existence and regularity for solutions of the Korteweg-de Vries equation
• On the Korteweg-de Vries equation
• Uniform stabilization of numerical schemes for the critical generalized Korteweg-de Vries equation with damping
• Decay and regularity in the inverse scattering problem
• Existence and uniqueness of solutions for the generalized Korteweg-de Vries equation
• Remarks on the Korteweg-de Vries equation
• Solutions of the Korteweg-de Vries equation in fractional order Sobolev spaces
• Solutions of the Korteweg-de Vries equation from irregular data
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• On Stability of Some Finite Difference Schemes for the Korteweg-de Vries Equation
• Convergence of a fully discrete finite difference scheme for the Korteweg–de Vries equation
• Uniqueness of Solutions for the Generalized Korteweg–de Vries Equation
• Convergence of Methods for the Numerical Solution of the Korteweg—de Vries Equation
• Korteweg‐devries equation and generalizations. VI. methods for exact solution
• The initial-value problem for the Korteweg-de Vries equation
• The Korteweg–deVries Equation: A Survey of Results
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Integrals of nonlinear equations of evolution and solitary waves
• Introduction to nonlinear dispersive equations