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Title: | A uniformly convergent scheme for two-parameter problems having layer behaviour |
Authors: | Kumar, Devendra |
Keywords: | Mathematics Singularly perturbed parabolic problems Two-parameter Collocation method Shishkin-type mesh |
Issue Date: | May-2021 |
Publisher: | Taylor & Francis |
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. |
URI: | https://www.tandfonline.com/doi/full/10.1080/00207160.2021.1925115 http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/10965 |
Appears in Collections: | Department of Mathematics |
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