Discretization and regularization of an inverse problem related to a quasilinear hyperbolic integrodifferential equation

An inverse problem for a one-dimensional quasilinear hyperbolic integrodifferential equation is reduced to a system of hyperbolic and second-kind integral equations. The obtained system is discretized by means of the method of finite differences. The convergence of the difference scheme in the case of small data is proved and the regularization of the inverse problem is discussed.