Boundary value problems, Initial value problems, Singular perturbations (Mathematics), Spline theory
A recent method for solving singular perturbation problems is examined. It is designed for the applied mathematician or engineer who needs a convenient, useful tool that requires little preparation and can be readily implemented using little more than an industry-standard software package for spreadsheets. In this paper, we shall examine singularly perturbed two point boundary value problems with the boundary layer at one end point. An initial-value technique is used for its solution by replacing the problem with an asymptotically equivalent first order problem, which is, in turn, solved as an initial value problem by using cubic splines. Numerical examples are provided to show that the method presented provides a fine approximation of the exact solution. The first chapter provides some background material to the cubic spline and boundary value problems. The works of several authors and a comparison of different solution methods are also discussed. Finally, some background into the specific singularly perturbed boundary value problems is introduced. The second chapter contains calculations and derivations necessary for the cubic spline and the initial value technique which are used in the solutions to the boundary value problems. The third chapter contains some worked numerical examples and the numerical data obtained along with most of the tables and figures that describe the solutions. The thesis concludes with some reflections on the results obtained and some discussion of the error bounds on the calculated approximations to the exact solutions for the numeric examples discussed
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Mohapatra, Ram N.
Master of Science (M.S.)
College of Sciences
Length of Campus-only Access
Masters Thesis (Open Access)
Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic
Negron, Luis G., "Initial-value Technique For Singularly Perturbed Two Point Boundary Value Problems Via Cubic Spline" (2010). Electronic Theses and Dissertations, 2004-2019. 1650.