Cauchy problem for the first order Quasi linear partial system of equations and numerical solution of the problem of compressible inviscid gas dynamics

In this thesis solution of theCauchy problem for systemof thepartial differential equationsof first order is investigated. In the first parttheoreticalstructure of the method of characteristics as for scalar equation as well as for the system ofequations areexplained. In the second partthe general solution of the system equations with constant coefficients is found, and then solution of the Cauchy problem for mentioned systemof equationsis obtained. In the third part the special method for finding the numerical solution in a class of discontinuous functions for the nonlinear system of equations, which describesthe flow of acompressible inviscidgasis suggested.Addition to, some properties of the numerical solution are studied. Using these thetheorem of convergence of the numerical solution to exact solution is proven.