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Comparison of high-accuracy finite-difference methods for linear wave propagation. (English) Zbl 0968.65061
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.
MSC:
65M06Finite difference methods (IVP of PDE)
78M20Finite difference methods (optics)
76Q05Hydro- and aero-acoustics
78A45Diffraction, scattering (optics)
76M20Finite difference methods (fluid mechanics)
35L15Second order hyperbolic equations, initial value problems
35Q60PDEs in connection with optics and electromagnetic theory
74J05Linear waves (solid mechanics)
74S20Finite difference methods in solid mechanics
65M20Method of lines (IVP of PDE)
65L06Multistep, Runge-Kutta, and extrapolation methods