Solving one class of systems of the polynomial volterra equations of the first kind by Newton's method

摘要

A known approach to the mathematical modeling of nonlinear dynamic systems (objects) of input-output type is based on the Volterra integro-power series. In this paper consideration is given to a numerical method of solving one class of systems of Volterra nonlinear integral equations which are associated with the problem of automatic control of a dynamic object with vector input and output. The algorithms to numerically solve these systems of equations are based on the Newton-Kantorovich method. Specific features of the algorithms are illustrated on the model examples. Reference dynamic system is represented by a mathematical model of transient process in the heat exchanger element.