The von Neumann analysis and modified equation approach for finite difference schemes

DOI10.1016/j.amc.2013.09.046zbMath1334.65133OpenAlexW2112741533MaRDI QIDQ275815

Zhicheng Yang, Jiequan Li

Publication date: 26 April 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2013.09.046

zbMATH Keywords

finite difference schemesamplification factorfull equivalencemodified equation approachvon Neumann analysis

Mathematics Subject Classification ID

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)

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Cites Work

• Unnamed Item
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• A critical analysis of the modified equation technique of warming and Hyett
• Dispersion-relation-preserving finite differene schemes for computational acoustics
• Analysis of a new high resolution upwind compact scheme
• The analysis of linear partial differential operators. III: Pseudo-differential operators
• The validity of the modified equation for nonlinear shock waves
• The modified equation approach to the stability and accuracy analysis of finite-difference methods
• On the method of modified equations. I: Asymptotic analysis of the Euler forward difference method
• Phase error and stability of second order methods for hyperbolic problems. II
• Phase error and stability of second order methods for hyperbolic problems. I
• Local oscillations in finite difference solutions of hyperbolic conservation laws
• Heuristic Modified Equation Analysis on Oscillations in Numerical Solutions of Conservation Laws
• Estimation of the Relaxation Factor for Small Mesh Size
• Survey of the stability of linear finite difference equations
• Group Velocity in Finite Difference Schemes
• On finite-difference approximations and entropy conditions for shocks
• Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows
• Numerical Solution of Partial Differential Equations
• On the Scope of the Method of Modified Equations
• Difference schemes for hyperbolic equations with high order of accuracy