ИСТИНА

We propose a numerical method for obtaining entropy solutions of a first-order quasilinear differential equation. It is possible to obtain an exact solution of the Cauchy problem under the following two restrictions. First, it is assumed that the flow function is piecewise linear, and second, it is required that the initial condition is a piecewise constant. We emphasize especially that nonconvex flow functions are also included in our method. The construction of solutions occurs through the motion of discontinuities, taking into account the known conditions of Hugoniot and Oleinik. The method is implemented as a computer program. In the report we provide examples and illustrations.