On the numerical study of nonlinear initial-boundary value problems or initial-value problems

DOI10.1016/S0096-3003(99)00216-7zbMath1024.65082OpenAlexW2092268774MaRDI QIDQ1854937

A. H. Nasser, Zaki F. A. El-Raheem

Publication date: 28 January 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(99)00216-7

zbMATH Keywords

error boundSchrödinger equationerror estimatedifference methodinverse scatteringnonlinear initial-boundary value problemsscattering methodnonlinear initial-value problemsBoussinesque systemsystem of hyper-elliptic type

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) NLS equations (nonlinear Schrödinger equations) (35Q55) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Cites Work

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• Regularity and uniqueness of solutions to the Boussinesq system of equations
• Asymptotic solutions of nonlinear evolution equations and a Painlevé transcedent
• Well-posed problems for some nonlinear dispersive waves
• A Finite Element Method for a Version of the Boussinesq Equation
• Lectures on the Inverse Scattering Transform
• Method for Solving the Korteweg-deVries Equation