Solving systems of linear Fredholm integro-differential equations with Fibonacci polynomials

In this paper, we introduce a method to solve systems of linear Fredholm integro-differential equations in terms of Fibonacci polynomials. First, we present some properties of these polynomials then a new approach implementing a collocation method in combination with matrices of Fibonacci polynomials is introduced to approximate the solution of high-order linear Fredholm integro-differentail equations systems with variable coefficients under the mixed conditions. Numerical results with comparisons are given to confirm the reliability of the proposed method for solving these systems of equations. (C) 2013 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.