Exact analysis of nonlinear instability in a discrete Burgers' equation

DOI10.1016/0021-9991(91)90039-NzbMath0746.65068OpenAlexW2040427805MaRDI QIDQ1181925

Milton Maritz, Schalk W. Schoombie

Publication date: 27 June 1992

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

Full work available at URL: https://doi.org/10.1016/0021-9991(91)90039-n

zbMATH Keywords

Burgers' equationnonlinear instabilityevolution difference equationsExact nonlinear stability conditionsexplicit difference equationsvon Neumann stability criterion

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 (1)

A Collocation Solution For Burgers Equation Using Quadratic B-Spline Finite Elements

Cites Work

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• Focusing: A mechanism for instability of nonlinear finite difference equations
• Propagation and stability of wavelike solutions of finite difference equations with variable coefficients
• On nonlinear instabilities in leap-frog finite difference schemes
• Studies in numerical nonlinear instability. II. A new look at \(u_ t+uu_ x=0\)
• Grid resonances, focusing and Benjamin-Feir instabilities in leapfrog time discretizations
• On modulational instabilities in discretisations of the Korteweg-de Vries equation
• On the generalization of the Cole-Hopf transformation
• Group velocity interpretation of the stability theory of Gustafsson, Kreiss, and Sundstroem
• A Hopscotch method for the Korteweg-de-Vries equation
• A generalised Cole-Hopf transformation for nonlinear parabolic and hyperbolic equations
• Instability of difference models for hyperbolic initial boundary value problems
• Studies in Numerical Nonlinear Instability I. Why do Leapfrog Schemes Go Unstable?
• Studies in Numerical Nonlinear Instability III: Augmented Hamiltonian Systems
• Convergence of Methods for the Numerical Solution of the Korteweg—de Vries Equation
• Group Velocity in Finite Difference Schemes
• On the Instability of Leap-Frog and Crank-Nicolson Approximations of a Nonlinear Partial Differential Equation
• The partial differential equation u_t + uu_x = μ_xx
• On a quasi-linear parabolic equation occurring in aerodynamics

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