Rasulov, MahirSinsoysal, Bahaddin2015-04-012015-04-012007Journal of Science and Technology 1 (1), 2007, 135-1451307-3818In this paper a new finite differences schemes of the Cauchy and initialboundary value problem, for the first order system differential equations which describe some conservation laws is suggested. At first an auxiliary problem which is equivalent to the main problem in certain sense is introduced. On the basis of the auxiliary problem the simple and economical algorithms from computational point of view are proposed.enArticle