This study focuses on the numerical solution of a challenging differential-difference equation within a dual boundary layer domain, employing an innovative fitted method. The equation is initially transformed into an ordinary singularly perturbed problem through a Taylor series expansion procedure. Subsequently, a three-term scheme is developed using finite differences, and the resulting tridiagonal system of equations is efficiently solved using the Thomas Algorithm. The study meticulously analyzes the accuracy of the solution by tabulating maximum absolute errors and employs graphical representations to illustrate the influence of fitting parameters on the layer structure. The research not only provides a practical numerical solution for complex problems but also contributes valuable insights into parameter sensitivity, facilitating precise adjustments for real-world applications. Additionally, the study advances the understanding of mathematical techniques, showcasing their adaptability in solving intricate problems encountered across various disciplines