Abstract
This article addresses interrelated integral nonlinear Volterra equations of the first and second kinds. Combining them, we obtain a system of integral equations with an identically degenerate matrix multiplying by the main part, which is usually called integral-algebraic equations. We highlight the fundamental features of the problems under consideration, namely their ill-posedness. We give conditions for the existence of a unique sufficiently smooth solution in terms of matrix pencils and propose an algorithm for their numerical solution, which is based on the simplest quadrature formula and linearization of a nonlinear integrand. Illustrative examples and results of numerical calculations of test examples are given.
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