Solution of differential algebraic equations with the Fredholm operator by the least squares method

Abstract This paper addresses systems of linear integral differential equations with a singular matrix multiplying the higher derivative of the desired vector-function. Such systems can be viewed as differential algebraic equations perturbed by the Fredholm operators. For such problems, we obtain solvability conditions and discuss the influence of small perturbations of the input data on the solution. Within the existence theorems, we propose the least squares method to obtain a numerical approximation.