A method for solving systems of conservation laws, which is a generalization of integro-interpolation method is proposed in this paper. We study the order of accuracy of the method for smooth solutions. The shock–entropy interaction problem, which contains strong discontinuities is solved by the proposed method. It is shown that the solution obtained by this method has a higher order than the solution obtained by the first-order scheme.

systems of conservation laws, order accurate scheme, discontinuous solution

Mathematical problems and theory of numerical methods