Difference methods for nonlinear first-order hyperbolic systems of equations

Abstract

Two difference methods for approximating some first-order nonlinear hyperbolic differential equations are considered. The methods apply to problems arising in a number of physical applications. Each of the methods is explicit and can be implemented on a computer easily. It is proved that the methods are first-order convergent in the maximum norm. For one of the methods in order to obtain convergence it is necessary to monitor, and perhaps change, the size of the time step as the computation proceeds. The other method is unconditionally convergent.