Numerical solution of a time dependent singularly perturbed delay differential equation on an exponentially graded mesh

P. Pramod Chakravarthy () and Meenakshi Shivhare ()
Additional contact information
P. Pramod Chakravarthy: Visvesvaraya National Institute of Technology
Meenakshi Shivhare: Presidency University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 4, 1329-1349

Abstract: Abstract In this article, we consider a singularly perturbed time-dependent reaction-diffusion problem with a large delay in space direction. The problem possess two boundary layers and also an interior layer. To find the numerical solution, we proposed a method which is comprised of an implicit Euler method in the time direction and a finite difference scheme on the exponentially graded mesh. The term containing the delay is treated using the theory of interpolation. The numerical method is shown to be first order parameter uniform convergent in space and time directions in the maximum norm. Theoretical estimates support the obtained numerical results.

Keywords: Singular perturbation problem; Partial differential equations; Delay differential equations; Finite difference method; Exponentially graded mesh; Parameter uniform convergence (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-023-00442-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:55:y:2024:i:4:d:10.1007_s13226-023-00442-x

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-023-00442-x

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().