Gunes, B.Duru, Hakki2025-05-102025-05-1020221023-61981563-512010.1080/10236198.2022.20432892-s2.0-85126039227https://doi.org/10.1080/10236198.2022.2043289https://hdl.handle.net/20.500.14720/14345We consider a singularly perturbed initial-third boundary value Sobolev problems. Firstly, the asymptotic behaviour of the exact solution is analysed. Then, a second-order finite difference scheme is constructed on the special non-uniform mesh. By using energy estimate, the stability and convergence of the proposed scheme are investigated in the discrete maximum norm. Finally, three numerical examples are solved to validate the theory.eninfo:eu-repo/semantics/closedAccessBakhvalov MeshError BoundsFinite Difference MethodSingular PerturbationSobolev ProblemArticle283Q3Q3385405WOS:000763180200001