An actual order of accuracy for several known numerical methods is studied for the case of hyperbolic-law discontinuous solutions. The approach in use is based on the convergence analysis of numerical solutions with various orders of differentiation. A wide class of difference schemes of first to fifth orders is analyzed. A number of recommendations on the application of higher-order finite difference schemes are given.

Keywords: hyperbolic conservation laws, TVD limiters, Runge-Kutta method, Riemann solvers, Godunov-type schemes, third-order scheme

• PostScript (in Russian) (3.14MB)
• PDF (in Russian) (425KB)



• PostScript. zip (in Russian) (635KB)
• PDF. zip (in Russian) (379KB)