Notes on the stability of a non-linear scheme for calculating the motion of a shock wave

Using generally accepted methods of linearizing non-linear equations with subsequent local stability analysis, it is shown that a difference scheme for calculating the shift of a shock wave region, presented in a certain paper relating to the Godunov method, is unstable if considered in isolation. A simple scheme which has no such drawback is discussed here, and the problem of extending the algorithm to more variables is analyzed.