Derivative instability of some schemes for the Korteweg-de Vries equation

DOI10.1016/S1007-5704(98)90075-2zbMath0921.65067OpenAlexW2081580058MaRDI QIDQ1288378

Jixiong Yu

Publication date: 16 September 1999

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s1007-5704(98)90075-2

zbMATH Keywords

KdV equationnumerical instabilityKorteweg-de Vries equationconserved quantityimplicit difference scheme

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)

Cites Work

• Unnamed Item
• Focusing: A mechanism for instability of nonlinear finite difference equations
• On nonlinear instabilities in leap-frog finite difference schemes
• On modulational instabilities in discretisations of the Korteweg-de Vries equation
• Numerical solution of K.D.V. equation
• Parametric excitation of computational modes inherent to leap-frog scheme applied to the Korteweg-de Vries equation
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Some results on the stability and dynamics of finite difference approximations to nonlinear partial differential equations
• Finite Amplitude Instabilities of Partial Difference Equations

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