Error estimate in the projection-difference method for an abstract quasilinear hyperbolic equation with a non-smooth right-hand side

S. E. Zhelezovsky

Saratov State Socio-Economic University

Abstract: We analyze the convergence of a three-level scheme of the projection-difference method for an abstract quasilinear hyperbolic equation in a Hilbert space with variable operator coefficients and a non-smooth (only Bochner integrable) right-hand side. We fix an energy error estimate without any special conditions imposed on the projection subspaces.

Key words: abstract hyperbolic equation, projection-difference method, error estimate.

UDC: 517.988.8

Received: 04.12.2007

 English version: Numerical Analysis and Applications, 2008, 1:2, 105–113