Table of Contents
Journal of Computational Methods in Physics
Volume 2016 (2016), Article ID 3698251, 5 pages
http://dx.doi.org/10.1155/2016/3698251
Research Article

On the Use of Recursive Evaluation of Derivatives and Padé Approximation to Solve the Blasius Problem

School of Computing, University of North Florida, Jacksonville, FL 32224, USA

Received 25 October 2015; Accepted 30 December 2015

Academic Editor: Mikhail Tokar

Copyright © 2016 Asai Asaithambi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Blasius problem is one of the well-known problems in fluid mechanics in the study of boundary layers. It is described by a third-order ordinary differential equation derived from the Navier-Stokes equation by a similarity transformation. Crocco and Wang independently transformed this third-order problem further into a second-order differential equation. Classical series solutions and their Padé approximants have been computed. These solutions however require extensive algebraic manipulations and significant computational effort. In this paper, we present a computational approach using algorithmic differentiation to obtain these series solutions. Our work produces results superior to those reported previously. Additionally, using increased precision in our calculations, we have been able to extend the usefulness of the method beyond limits where previous methods have failed.