On an effective solution of the Riemann problem for the second-order improperly elliptic equation in the rectangle

摘要

In this paper we present the numerical method for the solution of the Riemann problem for the second-order improperly elliptic equation. First, we reduce this problem to boundary value problems for properly elliptic equations, and after that we solve these problems by the grid method. MSC:35G45, 35G15, 35J25, 35J57, 65N06, 65N20.