Please use this identifier to cite or link to this item:
http://dspace.bits-pilani.ac.in:8080/jspui/xmlui/handle/123456789/10963
Title: | Trigonometric quintic B-spline collocation method for singularly perturbed turning point boundary value problems |
Authors: | Kumar, Devendra |
Keywords: | Mathematics Boundary layers Interior layers Shishkin-type mesh |
Issue Date: | Aug-2020 |
Publisher: | Taylor & Francis |
Abstract: | A trigonometric quintic B-spline method is proposed for the solution of a class of turning point singularly perturbed boundary value problems (SP-BVPs) whose solution exhibits either twin boundary layers near both endpoints of the interval of consideration or an interior layer near the turning point. To resolve the boundary/interior layer(s) trigonometric quintic B-spline basis functions are used with a piecewise-uniform mesh generated with the help of a transition parameter that separates the layer and regular regions. The proposed method reduces the problem into a system of algebraic equations which can be written in matrix form with the penta-diagonal coefficient matrix. The well-known fast penta-diagonal system solver algorithm is used to solve the system. The method is shown almost fourth-order convergent irrespective of the size of the diffusion parameter ϵ. The theoretical error bounds are verified by taking some relevant test examples computationally. |
URI: | https://www.tandfonline.com/doi/full/10.1080/00207160.2020.1802016 http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/10963 |
Appears in Collections: | Department of Mathematics |
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.