Propagation and stability of wavelike solutions of finite difference equations with variable coefficients

DOI10.1016/0021-9991(85)90167-6zbMath0584.65062OpenAlexW2141735783MaRDI QIDQ1069680

Michael B. Giles, W. T. jun. Thompkins

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0021-9991(85)90167-6

zbMATH Keywords

stability analysisasymptotic approachvariable coefficientspartial difference equationslocal group velocitymotion of wavepacketswavelike solutions

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Additive difference equations (39A10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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Parasitic waves and solitons in the numerical solution of the Korteweg-de Vries and modified Korteweg-de Vries equation ⋮ Developments and trends in three-dimensional mesh generation ⋮ Global spectral analysis: review of numerical methods ⋮ A quantum-like theory of wave propagation in periodic structures ⋮ Spurious scattering from discontinuously stretching grids in computational fluid dynamics ⋮ The nonlocal nature of internal reflection in computational fluid dynamics with spectral methods ⋮ Exact analysis of nonlinear instability in a discrete Burgers' equation ⋮ Error approximation in the solution of a linear PDE initial-value problem ⋮ On wave propagation in almost periodic structures ⋮ Development of high-order Taylor-Galerkin schemes for LES

Cites Work

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• Stability analysis of numerical boundary conditions and implicit difference approximations for hyperbolic equations
• Group velocity interpretation of the stability theory of Gustafsson, Kreiss, and Sundstroem
• Stability of Finite-Difference Models Containing Two Boundaries or Interfaces
• Boundary Approximations for Implicit Schemes for One-Dimensional Inviscid Equations of Gasdynamics
• Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems. II

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