A new operational approach for numerical solution of generalized functional integro-differential equations

In this paper, a class of linear and nonlinear functional integro-differential equations are considered that can be found in the various fields of sciences such as: stress–strain states of materials, motion of rigid bodies and models of polymer crystallization. The operational collocation method with shifted Jacobi polynomial bases is applied to approximate the solution of these equations. In addition, some theoretical results are given to simplify and reduce the computational costs. Finally, some numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.