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Linear bicharacteristic schemes without dissipation. (English) Zbl 0915.65106
The paper deals with non-dissipative numerical methods designed to compute the propagation of linear waves. They are inspired from the leapfrog methods developed in 1-D by A. Iserles [IMA J. Numer. Anal. 6, 381-392 (1986; Zbl 0637.65089)]. These methods are reviewed in the first part of the present paper. Their generalization to multidimensional problems requires some new ideas, based on the bicharacteristic equations and a staggered storage. The equations of acoustics, elastodynamics, and electromagnetics are treated this way, in two dimensions, and computional results are presented.
Reviewer: S.Benzoni (Lyon)

MSC:
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
74H45 Vibrations in dynamical problems in solid mechanics
76Q05 Hydro- and aero-acoustics
78A25 Electromagnetic theory (general)
35L15 Initial value problems for second-order hyperbolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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