Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Equation with Small Time Delay
In this article, a uniformly convergent numerical scheme is developed to solve a singularly perturbed convection-diffusion equation with a small delay having a boundary layer along the left side. A priori bounds of continuous solution and its derivatives are discussed. To solve the problem, the Cran...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2024/3772081 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this article, a uniformly convergent numerical scheme is developed to solve a singularly perturbed convection-diffusion equation with a small delay having a boundary layer along the left side. A priori bounds of continuous solution and its derivatives are discussed. To solve the problem, the Crank–Nicolson scheme in the time direction and the exponentially fitted finite difference scheme in the space direction are used. The stability of the method is analyzed. It is proved that the developed scheme converges uniformly with first order in space and second order in time. To validate the applicability of the theoretical finding of the developed scheme, numerical experiments are carried out by considering two test examples. |
|---|---|
| ISSN: | 1687-0425 |