News of the Kabardin-Balkar scientific center of RAS, 2007, Issue 3-1, Pages 88–96(Mi izkab743)
MATHEMATICS. MATHEMATIC MODELING
On convergence of the difference schemes which approximate the third boundary-value problem for an
hyperbolic equation in multidimensional domain with a
non-local boundary condition
Abstract:
A priori estimate in a difference interpretation for the solution of the third boundary-value problem for
third-order hyperbolic equations in a multidimensional domain with a non-local boundary-value condition
is obtained in this work. This implies the uniqueness and also the stability of the solution by initial data
and by the right-hand member in the norm $W_1^2 (G)$ on a layer. The convergence of the iterative process
for the considered non-local boundary-value problem in the small is proved.
References