A critical analysis of the modified equation technique of warming and Hyett

DOI10.1016/0021-9991(90)90093-GzbMath0689.65059OpenAlexW2073947237MaRDI QIDQ582024

Sin-Chung Chang

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0021-9991(90)90093-g

zbMATH Keywords

counterexamplesdifference methodsmodified equationNeumann stability analysis

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (16)

On balanced approximations for time integration of multiple time scale systems. ⋮ The von Neumann analysis and modified equation approach for finite difference schemes ⋮ Low-cost Runge-Kutta integrators for incompressible flow simulations ⋮ Asymptotic analysis of finite difference methods ⋮ Global spectral analysis: review of numerical methods ⋮ On the derivation of the modified equation for the analysis of linear numerical methods ⋮ Sparse identification of truncation errors ⋮ Equivalent partial differential equations of a lattice Boltzmann scheme ⋮ On the study of multilevel difference methods ⋮ Interpolation of infinite sequences by entire functions ⋮ Numerical solution of multidimensional hyperbolic PDEs using defect correction on adaptive grids ⋮ New numerical methods for Burgers' equation based on semi-Lagrangian and modified equation approaches ⋮ Analysis of a mixed semi-implicit/implicit algorithm for low-frequency two-fluid plasma modeling ⋮ On a superconvergent lattice Boltzmann boundary scheme ⋮ On the method of modified equations. I: Asymptotic analysis of the Euler forward difference method ⋮ Asymptotic analysis of the lattice Boltzmann equation

Cites Work

• 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 Scope of the Method of Modified Equations
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