Abstract and Applied Analysis 
Volume 2006 (2006), Article ID 14816, 13 pages
doi:10.1155/AAA/2006/14816

A note on the difference schemes for hyperbolic-elliptic equations

A. Ashyralyev,1 G. Judakova,2 and P. E. Sobolevskii3,4

 1Department of Mathematics, Fatih University, Buyukcekmece, Istanbul 34500, Turkey
2Department of Computer Sciences, Turkmen Politechnical Institute, Ashgabat, Turkmenistan
3Institute of Mathematics, Hebrew University, Jerusalem Givat Ram 91904, Israel
4Universidade Federal do Ceará, Brazil
Received 31 October 2004; Accepted 20 January 2005

Abstract

The nonlocal boundary value problem for hyperbolic-elliptic equation d2u(t)/dt2+Au(t)=f(t), (0≤t≤1), −d2u(t)/dt2+Au(t)=g(t), (−1≤t≤0), u(0)=ϕ, u(1)=u(−1) in a Hilbert space H is considered. The second order of accuracy difference schemes for approximate solutions of this boundary value problem are presented. The stability estimates for the solution of these difference schemes are established.