Yogesh Gupta, Manoj Kumar
Department of Mathematics
United College of Engineering and Management
Allahabad, 211010 (U.P.), INDIA
Department of Mathematics
Motilal Nehru National Institute of Technology
Allahabad, 211004 (U.P.) INDIA

Abstract. Spline methods provide an important tool to solve singularly perturbed boundary value problems. The present paper gives a comprehensive review of computational methods based on splines used in the solution of various classes of singularly perturbed problems such as self adjoint, linear, non-linear, semi-linear, quasi-linear, singular, single parameter and multi parameter. The spline based numerical techniques used by various researchers included in this paper can be classified as polynomial spline methods, non polynomial spline methods, B-spline methods, exponential spline methods and spline in tension methods. The emphasis of present paper is to accumulate the precis of recent works published during the years 2006-mid 2011 on spline methods for singular perturbation problems.

Received: August 27, 2011

AMS Subject Classification: 65L11, 65L60

Key Words and Phrases: singularly perturbed boundary value problems, polynomial splines, non-polynomial splines, B-splines, boundary layers, collocation method, nodal points

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