"Accuracy estimation and comparative analysis of difference schemes of high-order approximation"
Safronov A.V.

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

Safronov A.V. e-mail: p.grinevich@gmail.com