Numerical solution of singularly perturbed two-point boundary value problems by spline in tension
type: Item
instance of: scholarly article
title: Numerical solution of singularly perturbed two-point boundary value problems by spline in tension
zbMATH Open document ID: 1030.65087
DOI: 10.1016/S0096-3003(01)00146-1
author: M. K. Kadalbajoo
author: Kailash C. Patidar
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: Singularly perturbed boundary value problems for second-order ordinary differential equations are analyzed. In many situations equations of that type give rise to solutions possessing interior layers. The author uses spline approximation techniques to discretize the problem. With the help of a discrete maximum principle a convergence result uniformly in the singular perturbation parameter is proved. Moreover, a detailed discussion of the error term confirms that tension spline methods lead to accurate numerical solutions in the case when the step-size is large in respect to the singular perturbation parameter. Finally, numerical test examples are presented.
reviewed by: Johannes Schropp
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
zbMATH DE Number: 1861169
zbMATH Keywords: singular perturbation
zbMATH Keywords: boundary value problems
zbMATH Keywords: error bound
zbMATH Keywords: second-order differential equation
zbMATH Keywords: numerical examples
zbMATH Keywords: interior layers
zbMATH Keywords: convergence
zbMATH Keywords: tension spline methods
MaRDI profile type: Publication
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full work available at URL: s0096-3003(01)00146-1
OpenAlex ID: W2044768797
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description: scientific article; zbMATH DE number 1861169