Convergence of centered difference schemes for a system of two-dimensional equations of acoustics

The accuracy of difference schemes for first-order hyperbolic systems is studied for the case of two-dimensional equations of acoustics with various boundary conditions. A difference scheme is constructed and an a priori bound of the error is obtained in some weak norm. This bound combined with the Bramble-Hilbert theorem makes it possible to prove o(^m + h^m) convergence of the difference solution to the solution of the differential problem in the class W₂ ^m(Q_T, m=1,2.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 57, pp. 48–57, 1985.