Abstract and Applied Analysis (Jan 2006)

A note on the difference schemes for hyperbolic-elliptic equations

  • A. Ashyralyev,
  • G. Judakova,
  • P. E. Sobolevskii

DOI
https://doi.org/10.1155/AAA/2006/14816
Journal volume & issue
Vol. 2006

Abstract

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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.