Grid resonances, focusing and Benjamin-Feir instabilities in leapfrog time discretizations

DOI10.1016/0021-9991(88)90097-6zbMath0635.65108OpenAlexW2041993137MaRDI QIDQ1097658

B. George

Publication date: 1988

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(88)90097-6

zbMATH Keywords

instabilityparasitic wavesfocusing mechanismgrid resonanceleapfrog time discretizationspace semi- discretization

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

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Global spectral analysis: review of numerical methods, Localization and coherence in nonintegrable systems, Exact analysis of nonlinear instability in a discrete Burgers' equation, A numerical energy conserving method for the DNLS equation

Cites Work

• On nonlinear instabilities in leap-frog finite difference schemes
• Studies in numerical nonlinear instability. II. A new look at \(u_ t+uu_ x=0\)
• Resonances Introduced by Discretization
• Studies in Numerical Nonlinear Instability I. Why do Leapfrog Schemes Go Unstable?
• Finite Amplitude Instabilities of Partial Difference Equations
• On the Instability of Leap-Frog and Crank-Nicolson Approximations of a Nonlinear Partial Differential Equation
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