On the Numerical Solution of the Characteristic Problems for One Class of Quasilinear Equations

In this paper we present a numerical method to solve one class of quasilinear equations whose one of characteristics is straight line. One of the families of characteristics is completely determined, while the other depends on the first derivatives of unknown solution and thus is not determined in advance. The type of equation is hyperbolic with possible parabolic degeneracy and this fact should be taken into account so that the problems are posed correctly. For finding a numerical solution of the problems we propose an algorithm which is based on the well-known method of characteristics.