University of Guilan Journal of Mathematical Modeling 2345-394X 13 4 2025 12 01 Layer-resolving mesh method for convection-diffusion delay problems with boundary turning points 943 966 8909 10.22124/jmm.2025.30347.2724 EN Yimesgen Mehari Kebede Department of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia. Awoke Andargie Tiruneh Department of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia. Endalew Getnet Tsega Department of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia. Journal Article 2025 04 12 This paper introduces a numerical scheme designed to solve time-delay singularly perturbed parabolic convection-diffusion problems with turning points. A small parameter induces boundary layers, making standard methods ineffective. To tackle these challenges, we developed a layer-resolving numerical scheme using the Crank-Nicolson method (time) and a central finite difference method on a Shishkin mesh (space). The stability and parameter-uniform convergence analysis show that the error decreases quadratically. Numerical results demonstrate higher accuracy than existing approaches. https://jmm.guilan.ac.ir/article_8909_91aa4c961cf9f4c45d933b5710da27cf.pdf