Numerical Treatment of the Coupled Fredholm Integro-Differential Equations by Compact Finite Difference Method

The work introduces a novel numerical method for solving the Fredholm Integro-Differential Equations (FIDEs) and system of Fredholm Integro-Differential Equations (SFIDEs) by employing the fourth-order compact finite difference methods in conjunction with Simpson's quadrature rule.The accuracy of the proposed scheme is rigorously evaluated using 2 and norms, while the computational efficiency is measured by assessing the CPU-time values, demonstrating a notable reduction in computational cost compared to standard finite difference schemes.The significance of this approach lies in its ability to maintain high levels of accuracy, addressing a common challenge in traditional methods.The methods presented exhibit fourth accuracy in space, as evidenced by numerical experiments.The mentioned work signifies a notable progress in tackling problems related to FIDEs and SFIDEs.It introduces a robust and efficient numerical methodology that proves particularly effective in situations where obtaining exact solutions poses challenges.This advancement is crucial as it addresses a common difficulty faced in the solution of FIDEs and SFIDEs problems, offering a reliable numerical approach that can handle complex scenarios and contribute to more accurate and practical solutions in various fields of study.