Dispersion and Gibbs phenomenon associated with difference approximations to initial boundary-value problems for hyperbolic equations

In this paper, we analyze the problem of the semidiscretized approximation for the initial boundary-value problem of the wave equation. Point-wise convergence properties for the propagation of discontinuities are investigated via a uniformly valid asymptotic expansion. An approximate error analysis...

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Published inJournal of computational physics Vol. 18; no. 3; pp. 233 - 247
Main Author Chin, Raymond C.Y.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.1975
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Abstract In this paper, we analyze the problem of the semidiscretized approximation for the initial boundary-value problem of the wave equation. Point-wise convergence properties for the propagation of discontinuities are investigated via a uniformly valid asymptotic expansion. An approximate error analysis using matched asymptotic expansions is constructed and compared with the asymptotic expansion of the exact solution.
AbstractList In this paper, we analyze the problem of the semidiscretized approximation for the initial boundary-value problem of the wave equation. Point-wise convergence properties for the propagation of discontinuities are investigated via a uniformly valid asymptotic expansion. An approximate error analysis using matched asymptotic expansions is constructed and compared with the asymptotic expansion of the exact solution.
Author Chin, Raymond C.Y.
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Cites_doi 10.1002/cpa.3160190403
10.1147/rd.112.0215
10.1016/0021-9991(74)90099-0
10.1093/imamat/3.1.98
10.1137/0125036
10.1098/rsta.1954.0021
10.1016/0021-9991(74)90007-2
10.1090/S0025-5718-1969-0264862-4
10.1090/S0025-5718-1968-0233527-6
10.1137/0705031
10.1016/0041-5553(71)90168-6
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References Thomee (BIB5) 1971
Pearson (BIB4) 1969; 23
Bleistein (BIB17) 1967; 17
Apelkrans (BIB6) 1968; 22
Bateman (BIB12) 1944
Bleistein (BIB16) 1966; 14
Zhukov (BIB3) 1959; XIV
Hedstrom (BIB1) 1968; 5
Dean (BIB10) 1967; 3
Olver (BIB15) 1954; 247
Courant, Friedrichs, Lewy (BIB9) 1967
Synge (BIB11) 1973; 25
Orszag, Jayne (BIB7) 1974; 14
Abramowttz, Stegun (BIB13) 1964
Serdyukova (BIB2) 1971; 11
Chin (BIB8) 1974; 16
Chester, Friedman, Ursell (BIB14) 1957; 53
Chester (10.1016/0021-9991(75)90001-7_BIB14) 1957; 53
Orszag (10.1016/0021-9991(75)90001-7_BIB7) 1974; 14
Hedstrom (10.1016/0021-9991(75)90001-7_BIB1) 1968; 5
Serdyukova (10.1016/0021-9991(75)90001-7_BIB2) 1971; 11
Pearson (10.1016/0021-9991(75)90001-7_BIB4) 1969; 23
Dean (10.1016/0021-9991(75)90001-7_BIB10) 1967; 3
Olver (10.1016/0021-9991(75)90001-7_BIB15) 1954; 247
Bleistein (10.1016/0021-9991(75)90001-7_BIB17) 1967; 17
Abramowttz (10.1016/0021-9991(75)90001-7_BIB13) 1964
Synge (10.1016/0021-9991(75)90001-7_BIB11) 1973; 25
Chin (10.1016/0021-9991(75)90001-7_BIB8) 1974; 16
Apelkrans (10.1016/0021-9991(75)90001-7_BIB6) 1968; 22
Courant (10.1016/0021-9991(75)90001-7_BIB9) 1967
Thomee (10.1016/0021-9991(75)90001-7_BIB5) 1971
Zhukov (10.1016/0021-9991(75)90001-7_BIB3) 1959; XIV
Bleistein (10.1016/0021-9991(75)90001-7_BIB16) 1966; 14
Bateman (10.1016/0021-9991(75)90001-7_BIB12) 1944
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Snippet In this paper, we analyze the problem of the semidiscretized approximation for the initial boundary-value problem of the wave equation. Point-wise convergence...
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