@article{article_1600715, title={A Uniformly Convergent Difference Scheme for the Singularly Perturbed Periodic Problem}, journal={Bitlis Eren Üniversitesi Fen Bilimleri Dergisi}, volume={14}, pages={1348–1361}, year={2025}, DOI={10.17798/bitlisfen.1600715}, author={Cimen, Erkan}, keywords={Singular perturbation, Periodic problem, Finite difference method, Uniform convergence}, abstract={In this article, a novel numerical scheme is suggested to solve periodical boundary value problem for linear first order singularly perturbed equation. This scheme is constructed by the finite difference method on a special non-uniform mesh (Shishkin mesh) using quadrature rules with the remaining terms in integral form. It is proven that the scheme achieves almost first-order convergence on the discrete maximum norm. Finally, two test problems are considered to demonstrate the accuracy and performance of the method.}, number={3}, publisher={Bitlis Eren University}