Abstract
The paper is devoted to the study and numerical solution of linear systems of integral equations with an identically singular matrix in the principal part (called integral-algebraic equations). The systems studied in the paper are fundamentally different from those previously studied in that the upper and lower limits of integration are variable. These systems of equations will be referred to as integral-algebraic equations with variable integration limits. The paper develops and justifies an algorithm for a numerical solution of the first order of accuracy and establishes conditions for the existence of a unique continuous solution to the given problem. There are numerical computations provided for model examples.
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