183
Views
2
CrossRef citations to date
0
Altmetric
Section B

Numerical solution of a third-order nonlinear boundary-value problem by automatic differentiation

Pages 1484-1496 | Received 11 Jan 2010, Accepted 16 Aug 2010, Published online: 11 Mar 2011
 

Abstract

We develop a simple numerical method for obtaining Taylor series approximation to the solution of a nonlinear third-order boundary-value problem. We use recursive formulas derived from the governing differential equation itself to calculate exact values of the derivatives needed in the Taylor series. Since we do not use difference formulas or symbolic manipulation for calculating the derivatives, our method requires much less computational effort when compared with the techniques previously reported in the literature. We will illustrate the effectiveness of our method with several test problems.

2000 AMS Subject Classification :

Acknowledgements

The author would like to thank the anonymous reviewers for their valuable suggestions which greatly enhanced the quality of this paper.

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,129.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.