  We develop a numerical method for solving a system of nonlinear integral
equations involving two integral terms: at the current time t, one integral is
taken from 0 to t, and a different integral is taken from t to infinity. We
prove the convergence and the rate of convergence of our method. The
discretization results in an infinite-dimensional nonlinear system, and we also
prove results on the approximation of the solution of the infinite-dimensional
system by solution of finite truncations.
