Regularizing properties of difference schemes for singular integral-differential equations

Systems of integral-differential equations with a singular matrix multiplying the highest derivative of the unknown vector function are considered. An existence theorem is formulated, and a numerical solution method is proposed. The solutions to singular systems of integral-differential equations are unstable with respect to small perturbations in the initial data. The influence of initial perturbations on the behavior of numerical processes is analyzed. It is shown that the finite-difference schemes proposed for the systems under study are self-regularizing.