Numerical methods of Lagrange particle-points for one-dimensional gas dynamics wave equations

In the paper we consider the construction of numerical methods of computational gas dynamics based on the approximation of the second order nonlinear wave equations (NWE). Thes approach of "NWE” allows one to construct finite difference and finite elements schemes with cells of balance (conservative cells) both in the “finite volume” and lagrange “particle-points” framework. Therefore, numerical methods based on the approximations of NWE are of the great interest for the solution of one- and multi-dimensional problems of computational gas dynamics. In this paper the construction and investigation of discrete models of ”NWE” is performed for one dimensional gas dynamics problems in the Lagrange form and the results of numerical experiments are discussed.