A fitted numerical method for parabolic turning point singularly perturbed problems with an interior layer
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Date
2019
Journal Title
Journal ISSN
Volume Title
Publisher
Wiley
Abstract
The objective of this paper is to construct and analyzea fitted operator finite difference method (FOFDM) forthe family of time-dependent singularly perturbed parabolicconvection–diffusion problems. The solution to the problemswe consider exhibits an interior layer due to the presence ofa turning point. We first establish sharp bounds on the solu-tion and its derivatives. Then, we discretize the time variableusing the classical Euler method. This results in a system ofsingularly perturbed interior layer two-point boundary valueproblems. We propose a FOFDM to solve the system above.
Description
Keywords
Mathematics, Applied Mathematics, Problem
Citation
Munyakazi, J. B. et al. (2019). A fitted numerical method for parabolic turning point singularly perturbed problems with an interior layer. Numerical Methods for Partial Differential Equations, 35 (6) , 2407-2422. 10.1002/num.22420