High-order numerical solution for a class of nonlinear Fredholm integro-differential equations

The main objective of this work is to present a high-order numerical method to solve a class of nonlinear Fredholm integro-differential equations. By multiplying appropriate efficient factors and constructing an appropriate approximate function,  as well as employing a numerical integration method of order \gamma, the above-mentioned problem can be simplified to a nonlinear system of algebraic equations. Furthermore, we discuss the convergence analysis of the presented method in detail and demonstrate that it converges with an order \mathcal{O}(h^{۳.۵}) in the L^۲-norm. Some test examples are provided to demonstrate that the claimed order of convergence is obtained.

Keywords:

Efficient factors , Approximate function , Nonlinear algebraic system , Convergence analysis , Order of Convergence