Large oscillations arising in a dispersive numerical scheme

DOI10.1016/S0167-2789(96)00157-1zbMath0887.65098OpenAlexW2039016119MaRDI QIDQ2564795

C. David Levermore, Jian-Guo Liu

Publication date: 3 February 1997

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(96)00157-1

zbMATH Keywords

numerical experimentsdifference schemeoscillationsinviscid Burgers equationHopf equation

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 (10)

Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry ⋮ Dispersionless Toda and Toeplitz operators ⋮ Binary modulated oscillations in a semi-discrete version of Burgers equation ⋮ Finite genus solutions to the Ablowitz‐Ladik equations ⋮ Dissipative behavior of some fully nonlinear KdV-type equations ⋮ On discreteness of the Hopf equation ⋮ Numerical experiments on the modulation theory for the nonlinear atomic chain ⋮ Energy-Preserving and Stable Approximations for the Two-Dimensional Shallow Water Equations ⋮ Binary and ternary oscillations in a cubic numerical scheme ⋮ ENTROPY STABLE APPROXIMATIONS OF NAVIER–STOKES EQUATIONS WITH NO ARTIFICIAL NUMERICAL VISCOSITY

Cites Work

• Theory of nonlinear lattices
• On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices
• Macroscopic lattice dynamics
• On dispersive difference schemes
• Modulation of multiphase waves in the presence of resonance
• Accurate partial difference methods. II: Non-linear problems
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Dispersive approximations in fluid dynamics
• Instability of difference models for hyperbolic initial boundary value problems
• The Zero Dispersion Limit of the Korteweg-de Vries Equation With Periodic Initial Data
• On dispersive difference schemes. I
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
• The toda shock problem
• Dispersive Regularization of the Whitham Equation for the Toda Lattice
• The shock generation problem for a discrete gas with short-range repulsive forces
• Nonlinear differential–difference equations and Fourier analysis
• Numerical methods for oscillatory solutions to hyperbolic problems
• Finite genus solutions to the Ablowitz‐Ladik equations
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