Anthology of Spline Based Numerical Techniques for Singularly Perturbed Boundary Value Problems

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. AMS Subject Classification: 65L11, 65L60