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. Ashyralyev1,2 and P. E. Sobolevskii3

1Department of Mathematics, Fatih University, Istanbul, Turkey
2International Turkmen-Turkish University, Ashgabat, Turkmenistan
3Institute of Mathematics, Hebrew University, Jerusalem, Israel

Received 26 March 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.