The finite differences scheme for the first order system of nonlinear differential equations in a class of discontinuous functions

摘要

In this paper, the finite difference scheme for solving the Cauchy problem for the simplified Euler system in a class of discontinuous functions, which describes irrational flow of fluid by neglecting the viscosity and temperature effects is investigated. For this purpose, firstly the Euler system is decomposed with respect to its coordinates. Then an auxiliary problem which is superior to the main problem in terms of obtaining the solution is introduced, and the solutions of this auxiliary problem are smoother than the solutions of the main problem. Additionally, the auxiliary problem provides to develop effective and economical algorithms.