A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays

In this paper, a new numerical matrix-collocation technique is considered to solve functional integro-differential equations involving variable delays under the initial conditions. This technique is based essentially on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points. Some descriptive examples are performed to observe the practicability of the technique and the residual error analysis is employed to improve the obtained solutions. Also, the numerical results obtained by using these collocation points are compared in tables and figures.