Applications and methods for the numerical solution of a class of integer-algebraic equations with variable limits of integration

In the paper, we consider interrelated algebraic equations and Volterra linear integral equations of the first and second kind with variable limits of integration, where the lower limit of integration is strictly less than the upper limit for any values of the independent variable. If we combine these equations, we obtain a system of integral Volterra equations with variable limits of integration with an identically degenerate matrix in front of the principal part. Such systems of equations are usually called integro-algebraic equations with variable limits of integration. In this paper, without proof, sufficient conditions are given for the existence of a unique solution of integro-algebraic equations with variable limits of integration in the class of continuous functions. For a numerical solution of integro-algebraic equations with variable integration limits, a family of multistep methods based on explicit Adams quadrature formulas for the integral term and on extrapolation formulas for the principal part is proposed. The results of calculations of model examples that illustrate the effectiveness of the constructed methods are presented. As an appendix, the model of long-term development of the electric power system consisting of three types of non-atomic systems is considered: base stations on coal, base stations for oil, maneuver stations on gas and three types of nuclear power plants: with thermal neutron reactors on uranium, with fast neutron reactors On plutonium and with thermal neutron reactors on plutonium. The model is represented in the form of integro-algebraic equations with variable limits of integration. The article analyzes the described model of the long-term development of the electric power system, that is, the matching of the input data and the fulfillment of the conditions for the existence of a single continuous solution in terms of matrix beams.