MATRIX PROPERTIES OF FACTORIAL POLYNOMIALS AND APPLICATIONS TO OVERALL FUNCTIONAL INTEGRO DIFFERENTIAL EQUATIONS

In this study, by using the falling and rising factorial polynomials and the Stirling numbers of first and second kinds; the operational matrix characterizations of these expressions along with their derivatives and integrals are derived. Also, a typical matrix-collocation method based on the matrix relations of the mentioned polynomials is offered for solving the linear Volterra type integro-differential equations with functional delays. The approximate solutions are achieved in terms of the falling and rising factorial polynomials, thereby in the finite power series form. Additionally, a convergence criterion and an error technique related with the residual functions, together with three illustrative examples are created to reveal the efficiency of the method.