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

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.