Efficient numerical solution of linear Fredholm integro-differential equations via backward finite difference and Nyström methods

This paper presents a novel numerical approach for solving linear Fredholm integro-differential equations. We integrate the backward finite difference method with the Nyström method to reduce the system size by half compared to the method proposed by Tair et al. (J. Appl. Math. Comput. Mech. 20(3):53-64, 2021). This reduction enhances computational efficiency and is particularly advantageous for large integration intervals. Our method ensures convergence by constructing a new norm for \(\mathbb {R}^{N+1}\) ${\mathbb{R}}^{N+1}$ . Numerical tests demonstrate the superiority of our method in terms of execution time and accuracy. The results contribute to the ongoing efforts in solving integro-differential equations more effectively, offering a robust tool for applications in various scientific and engineering domains.