Abstract and Applied Analysis
Volume 6 (2001), Issue 2, Pages 63-70
doi:10.1155/S1085337501000501
A note on the difference schemes for hyperbolic equations
A. Ashyralyev1
and P.E. Sobolevskii2
1Department of Mathematics, Fatih University, Istanbul, Turkey
2Institute of Mathematics, Hebrew University, Jerusalem, Israel
Abstract
The initial value problem for hyperbolic equations d 2u(t)/dt 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.