Numerical Solution of the Fredholm Integro-Differential Equations Using High-Order Compact Finite Difference Method

This work aims to present a numerical method for solving Fredholm integro-differential equations (FIDE). This work discusses the use of a fourth and sixth-order compact finite difference method (CFDM) based on composite Boole’s rule to solve FIDE. The accuracy of the suggested schemes is computed through and norms and the efficiency of the approach is assessed through short CPU-time values. An important factor of the proposed methods is leading to a reduction in the computational cost of the schemes. This is a significant improvement over traditional methods, which often struggle to maintain high accuracy levels. The presented methods are shown to be the fourth and sixth order in space. Numerical experiments are presented to illustrate the performance of the suggested methods. Overall, the proposed method is a significant step forward in the field of solving FIDE problems. It offers a robust and efficient numerical approach that can achieve high levels of accuracy where exact solutions are hard to obtain.