A Parameter Uniform Scheme for Delay Parabolic Singularly Perturbed Turning Point Problem

• Published in: Differential equations and dynamical systems Vol. 32; no. 2; pp. 421 - 436
• Main Authors: Yadav, Swati, Rai, Pratima
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.04.2024; Springer Nature B.V
• Subjects: Boundary layers; Computer Science; Convection; Convergence; Engineering; Exact solutions; Mathematics; Mathematics and Statistics; Original Research; Twin boundary layers; 65M15; Shishkin mesh; 65M06; Turning point; 65M30; 65M12; Delay parabolic singular perturbed problem; Upwind scheme
• ISSN: 0971-3514; 0974-6870
• DOI: 10.1007/s12591-021-00577-5

This paper deals with an ε -uniform scheme for delay parabolic singularly perturbed problem (DPSPP). The considered problem is a convection–diffusion (C–D) type with the convection coefficient vanishing inside the domain. The turning point leads to the formation of two exponential boundary layers in the exact solution. We numerically solve the problem using the fitted mesh method and analyze the upwind scheme on a non-uniform mesh. We state some analytical results on the exact solution, which will be required in the convergence analysis of the proposed method. The proposed scheme has order of convergence almost one in space variable and one in time variable. The numerical findings practically support the theoretical results.