Abstract
Basing on Butkovskiy's fundamental integral equations in optimal control theory, in this paper a new method of solving the nonlinear integral equations is suggested, using an analog or hybrid computer device. The essential idea consists in an iterative procedure which can be carried out at a high rate of convergence compared with the computing time of a digital computer.As an application, the problem of optimal radiative heating a large body is considered, using the one-dimensional heat equation as a mathematical model. The temperature of the heating medium acting as a control function, there arises an essential non-linearity due to heat radiation. Butkovskiy's integral equations have been solved, using discrete approximation with respect to space.
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