NONE 20260427114350014 wseas/wseas content-registration-form+ja@crossref.org content-registration-form EQUATIONS 2944-9146 2732-9976 H. Nazan Çağlar Faculty of Applied Science Istanbul Nisantasi University Maslak Mahalesi, Taşyoncası Sokak, No: 1V ve No:1Y 34481742 Sarıyer-İstanbul TURKEY In this study, we apply local polynomial regression (LPR) to the solution of singularly perturbed delay differential equation with layer behavior. The method was tested using a numerical example to demonstrate its usefulness. The method presented in this paper was also compared with those developed by Ghomanjani et al.[1] and was found to be better. The proposed method was simple and computationally advantageous. The computed results we are compared with exact solutions. Plotted graphs of the solutions are also available in this study. 04 27 2026 04 27 2026 1 1 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/232021.2026.6.1 https://wseas.com/journals/equations/2026/a02equations-001(2026).pdf F.Ghomanjani, A.Kılıcaslan and F.A. Ghassabzade, Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavier, Abstract and Applied Analysis, (2014), oi: 10.1155/2014/731057. F. Ghomanjani, M. H. Farahi, and M. Gachpazan, Bezier ´ control points method to solve constrained quadratic optimal control of time varying linear systems, Computational & Applied Mathematics, 31(2012), pp. 433–456. F. Ghomanjani, A. Kılıcman, and S. Effati, Numerical solution for IVP in Volterra type linear integro-differential equations system, Abstract and Applied Analysis, (2013) , Article ID 490689. H. Caglar, N. Caglar, Solution of fifth order boundary value problems by using local polynomial regression, Applied Mathematics and Computation. 186 (2007), pp. 952-956. H. Caglar, N. Caglar, Numerical solution of integral equations by using local polynomial regression, Journal of Computational Analysis and Applications. 10(2008), pp.187-195. H. Caglar, N. Caglar, and B. Çağal,The numerical solution of partial differential equations with local polynomial regression(LPR), Journal of Computational Analysis and Applications. 11(2009), pp. 669-677. H. Caglar, N. Caglar, and M.Özer ,The Numerical Solution of Fractional Diffusion Equation by Using Local Polynomial Regression. 3rd International Congress on Advances in Applied Physics and Materials Science, 125(2013), pp. 551- 553., Doi: 10.12693/APhysPolA.125.551. H.Nazan Çağlar, S.Hikmet Çağlar, EH. Twizell The Numerical Solution of Third Order Boundary Value Problems With Fourth Degree B spline Functions, Intern.J.Computer Math, 71(1998), pp:373-381. P. Pramod Chakravarthy, S. Dinesh Kumar, R. Nageshwar Rao, Numerical Solution of Second Order Singularly Perturbed Delay Differential Equations via Cubic Spline in Tension, Int. J. Appl. Comput. Math. 3 (2017), pp:1703–1717 ,DOI 10.1007/s40819-016-0204-5 . J.Tsetimi, K.O. Ogeh and A.B. Disu, Modified Variational Iteration Method with Chebyshev Polynomials for Solving 12.th order Boundary Value Problems, Journal of Natural Science and Mathematics Research. 8 (2022), pp. 44-51.