A NOTE ON THE DIFFERENCE SCHEMES FOR HYPERBOLIC EQUATIONS

A NOTE ON THE DIFFERENCE SCHEMES FOR HYPERBOLIC EQUATIONS

The initial value problem for hyperbolic equations d 2 u ( t )/ d t 2 + A u ( t ) = f ( t )(0 ≤ t ≤ 1), u (0) = φ , u ′ (0) = ψ , in a Hilbert space H is considered. The first and second order accuracy difference schemes generated by the integer power of A approximately solving this initial value pr...

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Veröffentlicht in:Abstract and Applied Analysis 2001-01, Vol.2001 (2), p.63-70
Hauptverfasser: Ashyralyev, A., Sobolevskii, P. E.
Format: Artikel
Sprache:eng
Schlagworte:
34G
35L
65J
65N
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Zusammenfassung:The initial value problem for hyperbolic equations d 2 u ( t )/ d t 2 + A u ( t ) = f ( t )(0 ≤ t ≤ 1), u (0) = φ , u ′ (0) = ψ , in a Hilbert space H is considered. The first and second order accuracy difference schemes generated by the integer power of A approximately solving this initial value problem are presented. The stability estimates for the solution of these difference schemes are obtained.
ISSN:1085-3375
1687-0409
DOI:10.1155/S1085337501000501