Difference schemes with a splitting operator for systems of first-order hyperbolic equations

Abstract

WE construct difference schemes with a splitting operator which approximate with order O(τ + ¦h¦ 2) a first-order system of hyperbolic equations and a system of equations of the mixed type for which a Cauchy problem periodic in the space variables is established. Stability in L 2 on a layer is proved for the solution of these schemes. In this note we consider a difference scheme with a splitting operator, approximating with order O(τ + ¦h¦ 2) a system of first-order hyperbolic equations for which we establish a Cauchy problem, periodic in the space variables, and for the solution of which stability is proved. The proposed scheme is similar to the difference scheme for parabolic equations studied in [1,2], and can easily be transferred to the case of a system of equations of the mixed type, considered in [3, 4]. Difference schemes for first-order systems and equations of hyperbolic type were considered in [5–7] and in a number of other papers.