Application of Fibonacci collocation method for solving Volterra–Fredholm integral equations

In this paper, a new matrix method based on Fibonacci polynomials and collocation points is proposed for numerically solving the Volterra–Fredholm integral equations. In fact, the approximate solution of the problem in the truncated Fibonacci series form is obtained by this method. Also, convergence analysis of the proposed method is provided under several mild conditions. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.