On the Efficient Approach for the Solution of General Second Order Linear and Nonlinear Fredholm Integro-Differential Equations

Abstract

In this paper, Fredholm integro-differential equations are solved using the derivative of the Lucas polynomials in matrix form. The equation is first transformed into systems of nonlinear algebraic equations using the Lucas polynomials. The unknown parameters required for approximating the solution of Fredholm integro-differential equations are then determined using Gaussian elimination. The method has proven to be an active and dependable technique for solving many Fredholm integro-differential equations of different order. The novelty in this technique is that it is capable of solving Fredholm integro differential equation of any order by simply updating the matrix of derivative of the Lucas polynomials also surprisingly the technique was tried on mix Fredholm-Volterra integro differential equation and the result obtained was amazing. Some test problems contained in the literature were solved using the developed technique and the results confirmed the applicability and efficiency of the method. The accuracy of the method was observed to be better when compared with some existing methods.