Numerical method based on sinc functions for solving singularly perturbed Fredholm integro-differential equations

A numerical method based on sinc functions is developed and examined to approximate the solution of singularly perturbed Fredholm integro-differential equations. This method involves combining sinc basis functions with nonclassical weight functions. With this method, the difficulty of the non-differentiability of the sinc function at the boundary points has been solved. A major challenge in solving these equations is the presence of the small parameter ε, which introduces stiffness. The sinc method effectively overcomes this issue, achieving an exponential rate of convergence. Furthermore, to demonstrate the efficiency and accuracy of the proposed method, several examples are solved and compared with other existing methods. Numerical results confirm the exponential convergence order of the proposed method obtained with theoretical results.