To justification of the integral convergence method for studying the finite-difference schemes accuracy

We justified the method of integral convergence for studying the accuracy of finitedifference shock-capturing schemes for numerical simulation of shock waves propagating at a variable speed. The order of integral convergence is determined using a series of numerical calculations on a family of embedded difference grids. It allows us to model a space-continuous difference solution of the corresponding Cauchy problem. This approach is used to study the accuracy of explicit finite-difference schemes such as Rusanov scheme, TVD and WENO schemes, which have a higher order of classic approximation, as well as an implicit compact scheme with artificial viscosity of the fourth order of divergence, which has a third order of both classic and weak approximation.