A systematic approach for correcting nonlinear instabilities: The Lax- Wendroff scheme for scalar conservation laws
From MaRDI portal
Publication:1242660
DOI10.1007/BF01398510zbMath0368.65048OpenAlexW2439399157WikidataQ114852664 ScholiaQ114852664MaRDI QIDQ1242660
Stanley J. Osher, Andrew J. Majda
Publication date: 1978
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/132561
Hyperbolic conservation laws (35L65) 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 (18)
Shock capturing, level sets, and PDE based methods in computer vision and image processing: A review of Osher's contributions ⋮ Modified equation techniques for reactive-diffusive systems. I: Explicit, implicit and quasilinear methods ⋮ Studies in numerical nonlinear instability. II. A new look at \(u_ t+uu_ x=0\) ⋮ Strong Stability Preserving Integrating Factor Runge--Kutta Methods ⋮ Steady discrete shocks of 5th and 7th-order RBC schemes and shock profiles of their equivalent differential equations ⋮ Galilean invariance and the conservative difference schemes for scalar laws ⋮ A Comparison of Analytical Solutions of a High-Order RBC Scheme and Its Equivalent Differential Equation for a Steady Shock Problem ⋮ High order strong stability preserving time discretizations ⋮ Stable Viscosities and Shock Profiles for Systems of Conservation Laws ⋮ The method of fractional steps for conservation laws ⋮ Convergence of difference schemes with high resolution for conservation laws ⋮ Stable and accurate hybrid finite volume methods based on pure convexity arguments for hyperbolic systems of conservation law. ⋮ An implicit scheme for nonlinear evolution equations ⋮ Sparse identification of truncation errors ⋮ Particle methods revisited: a class of high order finite-difference methods ⋮ High-Order Schemes and Entropy Condition for Nonlinear Hyperbolic Systems of Conservation Laws ⋮ On two upwind finite-difference schemes for hyperbolic equations in non- conservative form ⋮ The validity of the modified equation for nonlinear shock waves
Cites Work
- Unnamed Item
- Unnamed Item
- The modified equation approach to the stability and accuracy analysis of finite-difference methods
- A detached shock calculation by second-order finite differences
- Models of Difference Schemes for u t + u x = 0 by Partial Differential Equations
- The artificial compression method for computation of shocks and contact discontinuities. I. Single conservation laws
- On finite-difference approximations and entropy conditions for shocks
- Systems of conservation laws
- On the Instability of Leap-Frog and Crank-Nicolson Approximations of a Nonlinear Partial Differential Equation
This page was built for publication: A systematic approach for correcting nonlinear instabilities: The Lax- Wendroff scheme for scalar conservation laws
