A numerical scheme for solving integral equations which exploits the capability of modern computers to integrate systems of several hundred or several thousand simultaneous ordinary differential equations subject to known initial conditions. The scheme is based on the conversion of a basic integral equation of transport theory into initial-value problems. Inverse problems, which involve estimating properties of the sources of the radiation field and the medium, given certain observations on the solution of the radiation field, are viewed as nonlinear multipoint boundary-value problems that can be solved numerically by a quasilinearization technique. Results of numerical experiments are included, as well as numerous references to other works on the subject. The study should be of particular interest to meteorologists, physicists, and numerical analysts. 39 pp. Refs.