This article is cited in 8 papers

Вычислительные методы и приложения

Accuracy estimation and comparative analysis of difference schemes of high-order approximation

A. V. Safronov

The Central Research Institute of Machinery

Abstract: 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.

UDC: 519.6