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Zbl 0968.65061
Zingg, David W.
Comparison of high-accuracy finite-difference methods for linear wave propagation. (English)
[J] SIAM J. Sci. Comput. 22, No.2, 476-502 (2000). ISSN 1064-8275; ISSN 1095-7197/e

The paper deals with finite difference methods for numerical simulation of the linear wave propagation and scattering (electromagnetism, acoustics, elastic waves). The attention is paid to nondissipative schemes (i.e., to the schemes produce no amplitude error) and schemes with the controlled numerical dissipation. The author analyzes several numerical schemes -- compact schemes, noncompact schemes, schemes on staggered grids, and schemes optimized to produce specific characteristics. The studied time-marching methods include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. The fully-discrete methods are also analyzed. Numerical tests are presented to compare the studied methods and to provide understanding.
[Marek Brandner (Plzeň)]
MSC 2000:
*65M06 Finite difference methods (IVP of PDE)
78M20 Finite difference methods (optics)
76Q05 Density waves (fluid mechanics)
78A45 Diffraction, scattering (optics)
76M20 Finite difference methods
35L15 Second order hyperbolic equations, initial value problems
35Q60 PDE of electromagnetic theory and optics
74J05 Linear waves
74S20 Finite difference methods
65M20 Method of lines (IVP of PDE)
65L06 Multistep, Runge-Kutta, and extrapolation methods

Keywords: finite difference schemes; wave propagation; electromagnetism; acoustics; Maxwell equations; numerical examples; comparison of methods; scattering; elastic waves; nondissipative schemes; numerical dissipation; compact schemes; noncompact schemes; staggered grids; time-marching methods; Runte-Kutta methods; Adams-Bashforth methods; leapfrog method

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