Multi-step methods for the numerical solution of integro-algebraic equations with two singularities in the kernel

We consider a class of Volterra integro-algebraic equations with two integrable power singularities in the kernel and indicate fundamental difficulties in studying such equations. In terms of matrix pencils, we formulate sufficient conditions for the existence of a unique continuous solution. Also, we propose multi-step methods for solving such equations based on the method of integrating products and Adams quadrature formulas and present the results of numerical experiments.