dc.contributor.author |
Kumar, Devendra |
|
dc.date.accessioned |
2023-07-22T04:40:07Z |
|
dc.date.available |
2023-07-22T04:40:07Z |
|
dc.date.issued |
2021-05 |
|
dc.identifier.uri |
https://www.tandfonline.com/doi/full/10.1080/00207160.2021.1925115 |
|
dc.identifier.uri |
http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/10965 |
|
dc.description.abstract |
We present a numerical scheme for the solution of two-parameter singularly perturbed problems whose solution has multi-scale behaviour in the sense that there are small regions where the solution changes very rapidly (known as layer regions) otherwise the solution is smooth (known as a regular region) throughout the domain of consideration. In particular, to solve the problems whose solution exhibits twin boundary layers at both endpoints of the domain of consideration, we propose a collocation method based on the quintic B-spline basis functions. A piecewise-uniform mesh that increases the density within the layer region compared to the outer region is used. An (N+1)×(N+1) penta-diagonal system of algebraic equations is obtained after the discretization. A well-known fast penta-diagonal system solver algorithm is used to solve the system. We have shown that the method is almost fourth-order parameters uniformly convergent. The theoretical estimates are verified through numerical simulations for two test problems. |
en_US |
dc.language.iso |
en |
en_US |
dc.publisher |
Taylor & Francis |
en_US |
dc.subject |
Mathematics |
en_US |
dc.subject |
Singularly perturbed parabolic problems |
en_US |
dc.subject |
Two-parameter |
en_US |
dc.subject |
Collocation method |
en_US |
dc.subject |
Shishkin-type mesh |
en_US |
dc.title |
A uniformly convergent scheme for two-parameter problems having layer behaviour |
en_US |
dc.type |
Article |
en_US |