On an Algorithm for the Numerical Solution of Integral-Algebraic Equations - Bulatov, M. V. (Lobachevskii journal of mathematics, 2023)
The article addresses linear systems of Volterra integral equations with sufficiently smooth input data and an identically degenerate matrix in front of the main part. Difficulties arising in the qualitative study of these problems and the construction of numerical methods for their solution are emphasized. The class of systems under consideration that have a unique sufficiently smooth solution is singled out in terms of matrix pencils. The simplest family of collocation-variational algorithms for this type of problem is proposed. The numerical calculations of model examples are presented.