Inverse coefficient problems for a first order hyperbolic system

In this paper, the direct and inverse initial boundary value problems for a first order system of two hyperbolic equations are considered. The method of characteristics and the finite difference method are applied to the theoretical and numerical solutions of the direct problem, respectively. Moreover the suitability of the method of characteristics for the inverse problem of finding solely space-dependent coefficients and the finite difference method for solely time-dependent coefficients of the first order hyperbolic system are shown. The stability of the numerical method is supported by the examples.