Method of Lines for Hyperbolic Differential Equations

DOI10.1137/0729041zbMath0754.65078OpenAlexW2048526316MaRDI QIDQ4008959

Godela Scherer, Heinz-Otto Kreiss

Publication date: 27 September 1992

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0729041

zbMATH Keywords

method of linesRunge-Kutta methodsstability regionstiff ordinary differential equation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Initial value problems for first-order hyperbolic systems (35L45)

Related Items (11)

Conjugate heat transfer for the unsteady compressible Navier-Stokes equations using a multi-block coupling ⋮ Boundary conditions for coupled quasilinear wave equations with application to isolated systems ⋮ Numerical stability for finite difference approximations of Einstein's equations ⋮ The method of lines for hyperbolic stochastic functional partial differential equations ⋮ Runge-Kutta integration of the equal width wave equation using the method of lines ⋮ Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form ⋮ On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity ⋮ Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space ⋮ Grid stabilization of high-order one-sided differencing. II: Second-order wave equations ⋮ Operator bounds and time step conditions for the DG and central DG methods ⋮ On the stability definition of difference approximations for the initial boundary value problem

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