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Adaptive mesh generation for singularly perturbed fourth-order ordinary differential equations

Das, Pratibhamoy and Natesan, Srinivasan (2015) Adaptive mesh generation for singularly perturbed fourth-order ordinary differential equations. In: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 92 (3). pp. 562-578.

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Official URL: http://dx.doi.org/10.1080/00207160.2014.902054

Abstract

In this paper, we consider a singularly perturbed boundary-value problem for fourth-order ordinary differential equation (ODE) whose highest-order derivative is multiplied by a small perturbation parameter. To solve this ODE, we transform the differential equation into a coupled system of two singularly perturbed ODEs. The classical central difference scheme is used to discretize the system of ODEs on a nonuniform mesh which is generated by equidistribution of a positive monitor function. We have shown that the proposed technique provides first-order accuracy independent of the perturbation parameter. Numerical experiments are provided to validate the theoretical results.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to the TAYLOR & FRANCIS LTD, 4 PARK SQUARE, MILTON PARK, ABINGDON OX14 4RN, OXON, ENGLAND
Keywords: 65L10; G.1.7; adaptively generated mesh; uniform convergence; fourth-order ODE; grid equidistribution; singularly perturbed boundary-value problems; boundary layers
Department/Centre: Division of Interdisciplinary Research > Supercomputer Education & Research Centre
Depositing User: Id for Latest eprints
Date Deposited: 14 Feb 2015 13:32
Last Modified: 14 Feb 2015 13:32
URI: http://eprints.iisc.ac.in/id/eprint/50801

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