Numerical Solution of High-Order Linear Fredholm Integro-Differential Equations by Lucas Collocation Method

Abstract

In this paper, a useful matrix approach for high-order linear Fredholm integro-differential equations with initial boundary conditions expressed as Lucas polynomials is proposed. Through the use of a matrix equation which is equivalent to a set of linear algebraic equations—the method transforms the integro differential equation. When compared to other methods that have been proposed in the literature, the numerical results from the suggested technique reveal that it is effective and promising, and error estimation of the scheme was derived. These results were compared with the exact solutions to the tested issues.