Survey of the Layer Behaviour of the Singularly Perturbed Fredholm Integro-Differential Equation

The work handles a second order linear singularly perturbed Fredholm integro differential equation. The qualitative analysis of such problems is quite difficult due to the rapid change in behavior of the solution within the boundary layer. In this study, asymptotic estimates for the solution and its first and second derivatives of the Fredholm integro differential equation with a boundary layer have been presented. The obtained estimates have significance in their contribution to the development and evaluation of appropriate approximate methods in mathematical modeling and analysis. Furthermore, the presented example provides support for the validity of the theoretical results and the accuracy of the estimates.