The new alternating direction implicit difference methods for the wave equations

DOI10.1016/j.cam.2008.11.001zbMath1166.65044OpenAlexW2072034576MaRDI QIDQ1026447

Jinggang Qin

Publication date: 25 June 2009

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

Full work available at URL: https://doi.org/10.1016/j.cam.2008.11.001

zbMATH Keywords

wave equationnumerical examplesunconditional stabilityerror analysisoperator splittingcompact difference schemealternating direction implicit (ADI) scheme

Mathematics Subject Classification ID

Wave equation (35L05) 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) Iterative numerical methods for linear systems (65F10) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (9)

An explicit fourth-order compact difference scheme for solving the 2D wave equation ⋮ An alternating direction implicit method for a second-order hyperbolic diffusion equation with convection ⋮ Large-amplitude elastic free-surface waves: geometric nonlinearity and peakons ⋮ High-order compact ADI method using predictor-corrector scheme for 2D complex Ginzburg-Landau equation ⋮ A high accuracy local one-dimensional explicit compact scheme for the 2D acoustic wave equation ⋮ HOC-ADI schemes for two-dimensional Ginzburg-Landau equation in superconductivity ⋮ Compact finite difference modeling of 2-D acoustic wave propagation ⋮ Alternating direction implicit time integrations for finite difference acoustic wave propagation: parallelization and convergence ⋮ Alternating direction implicit method for solving two-dimensional cubic nonlinear Schrödinger equation

Cites Work

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• High-order schemes for acoustic waveform simulation
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• A general formulation of alternating direction methods. I: Parabolic and hyperbolic problems
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• An explicit fourth-order compact finite difference scheme for three-dimensional convection-diffusion equation
• Compact ADI method for solving parabolic differential equations
• IMPROVED ACCURACY FOR LOCALLY ONE-DIMENSIONAL METHODS FOR PARABOLIC EQUATIONS
• A compact fourth‐order finite difference scheme for the steady incompressible Navier‐Stokes equations

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