Finite Differences Scheme for the Euler System of 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 discountin-uous 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 superiour to the main problem in terms of obtaining the solution is introduced, and shown that the solutions of this auxiliary problem are smoother than the solutions of the main problem. Additionally, the auxiliary problem provides to develop effective and efficient algorithms.