Numerical Analysis and Applicable Mathematics
Title
Using the Kellogg-Tsan Solution Decomposition in Numerical Methods for Singularly Perturbed Convection Diffusion Problems
Authors
Relja Vulanovi'c*a and Thái Anh Nhanb
aDepartment of Mathematical Sciences, Kent State University at Stark, 6000 Frank Ave. NW, North Canton, OH 44720, USA
bDepartment of Mathematics and Science, Holy Names University, 3500 Mountain Blvd., Oakland, CA 94619, USA
*Corresponding author E-mail address: rvulanov@kent.edu (Relja Vulanovic)
Article History
Publication details: Received: 24th April 2020; Revised: 11th June 2020; Accepted: 15th June 2020; Published: 19th June 2020
Cite this article
Vulanovic R.; Nhan T. A. Using the Kellogg-Tsan Solution Decomposition in Numerical Methods for Singularly Perturbed Convection Diffusion Problems. Numer. Anal. Appl. Math., 2020, 1(1), 1-9.
Abstract
The linear one-dimensional singularly perturbed convection-diffusion problem is solved numerically by a second-order method that is uniform in the perturbation parameter". The method uses the Kellogg-Tsan decomposition of the continuous solution. This increases the accuracy of the numerical results and simplifies the proof of their"-uniformity
Keywords
singular perturbation; convection-diffusion; Kellogg-Tsan solution decomposition; Vulanovi'c Bakhvalov mesh; finite differences; uniform convergence.
