Stability of method of characteristics (Q1807705)

The Lyapunov functional method is used to verify the stability of a system of two first-order hyperbolic partial differential equations. Initial and boundary conditions are assumed. In the case considered Hurwitz type stability occurs simultaneously with Schur type stability. The method of characteristics is used to approximate a continuous system. It is shown that the stability conditions for discrete approximation result from the stability conditions for the continuous system. The stability of the continuous system is easier to verify than the stability of its discrete approximation. This observation leads to the conclusion that the stability of the continuous system ought to be considered in order to insure convergence of the discrete approximations to the solution of the original problem. A new method for the experimental choice of grid density is proposed. A numerical example is presented in the last part of the paper.