University of Tabriz Computational Methods for Differential Equations 2345-3982 Articles in Press 2025 05 06 Robust finite difference schemes for one dimensional parabolic singularly perturbed problem with regular layers 19778 10.22034/cmde.2025.63398.2828 EN Kishun Kumar Sah Department of Mathematics, National Institute of Technology Patna, India. Subramaniam Gowrisankar Department of Mathematics, National Institute of Technology Patna, India. Journal Article 2024 09 08 In this article, we study the midpoint finite difference scheme for the singularly perturbed parabolic convection diffusion problem on non-uniform meshes, which are determined by a generating function with the boundary layer on the right side of the domain. The non-uniform meshes considered in this are the classical Shishkin meshes, Shishkin-Bakhvalov meshes, and Shishkin-Bakhvalov modified meshes. Uniform convergence are established with respect to the perturbation parameter on the non-uniform meshes. The backward Euler scheme is applied in the time direction and midpoint finite schemes in the space. Uniform convergence of upto second order in the space and first order in time are obtained. Two numerical examples are considered to validate the numerical and theoretical results obtained. https://cmde.tabrizu.ac.ir/article_19778_5024af9b26a03342e393198807e44f9a.pdf