On the practical use of high-order methods for hyperbolic systems

DOI10.1016/0021-9991(80)90073-XzbMath0424.65051MaRDI QIDQ1135094

Eli Turkel

Publication date: 1980

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

zbMATH Keywords

hyperbolic systemshigh-order methodsspectral methodswave propagation phenomenaasymptotic approach to a steady statesmooth and shocked flows

Mathematics Subject Classification ID

Shock waves and blast waves in fluid mechanics (76L05) Error bounds for boundary value problems involving PDEs (65N15) Wave equation (35L05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Initial-boundary value problems for first-order hyperbolic systems (35L50) Initial value problems for first-order hyperbolic systems (35L45) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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Cites Work

• Unnamed Item
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• On a high accuracy finite difference method
• Multidimensional difference schemes with fourth-order accuracy
• An implicit finite-difference algorithm for hyperbolic systems in conservation-law form
• On boundary conditions for hyperbolic difference schemes
• An implicit, compact, finite difference method to solve hyperbolic equations
• The operator compact implicit method for parabolic equations
• Phase error and stability of second order methods for hyperbolic problems. I
• Alternating direction implicit techniques for two-dimensional magnetohydrodynamic calculations
• On difference schemes of third order accuracy for nonlinear hyperbolic systems
• Third order difference methods for hyperbolic equations
• On the numerical solution of elliptic partial differential equations by the method of lines
• Accurate partial difference methods. I: Linear Cauchy problems
• Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems. II
• The Relative Efficiency of Finite Difference and Finite Element Methods. I: Hyperbolic Problems and Splines
• The Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems
• Difference Schemes with Fourth Order Accuracy for Hyperbolic Equations
• Higher-Order Numerical Solutions Using Cubic Splines
• On a Fourier Method for the Integration of Hyperbolic Equations
• Propagation of error into regions of smoothness for accurate difference approximations to hyperbolic equations
• Dissipative Two-Four Methods for Time-Dependent Problems
• Fourth Order Difference Methods for the Initial Boundary-Value Problem for Hyperbolic Equations
• On the Construction and Comparison of Difference Schemes
• Solutions with shocks: An example of an L₁‐contractive semigroup
• Numerical Simulation of Incompressible Flows Within Simple Boundaries. I. Galerkin (Spectral) Representations