Lucas’s Matrix Approach in Solving First Order Linear Volterra Integro-Differential Equations

Abstract

In this paper, matrix calculus of the Lucas polynomials is derived for the numerical solution of first order linear Volterra integro-differential equations. The equation is solved by transforming the differential part of the equation using the Lucas polynomials matrix of derivatives and the integral part is evaluated base on the Lucas polynomials function. The new method possesses the desirable feature of being a strong and dependable technique for solving many Volterra integro-differential equations of the first order. The developed technique was illustrated on some test problems in literature and results confirmed that the developed technique is more accurate than those developed by some considered authors