A numerical solution of singularly perturbed Fredholm integro-differential equation with discontinuous source term

In this paper, we investigate a singularly perturbed Fredholm integro-differential problem with a discontinuous source term, leading to the formation of interior layers in the solution at the point of discontinuity. We apply the exponentially fitted mesh method to solve the problem. Our analysis demonstrates that the method exhibits almost first-order convergence in the maximum norm, independent of the diffusion parameter. Numerical experiments are conducted to verify the validity of our theoretical results and they support the accuracy of our estimates.