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Spatial discretization of hyperbolic equations with periodic solutions
Author(s) -
van der Houwen P. J.
Publication year - 1986
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620230802
Subject(s) - discretization , mathematics , mathematical analysis , interval (graph theory) , hyperbolic partial differential equation , cauchy distribution , fourier transform , fourier series , partial differential equation , combinatorics
We investigate the Cauchy problem for hyperbolic equations for which the frequencies of the main Fourier components in the solution are located in a given frequency interval. Difference formulae for the spatial derivatives are constructed that are tuned to the given intervals of frequencies. Numerical examples illustrating these special discretizations are given both for linear and non‐linear problems.