Abstract and Applied Analysis

Numerical Solution of Higher Order Boundary Value Problems

Shahid S. Siddiqi and Muzammal Iftikhar

Full-text: Open access

Abstract

The aim of this paper is to use the homotopy analysis method (HAM), an approximating technique for solving linear and nonlinear higher order boundary value problems. Using HAM, approximate solutions of seventh-, eighth-, and tenth-order boundary value problems are developed. This approach provides the solution in terms of a convergent series. Approximate results are given for several examples to illustrate the implementation and accuracy of the method. The results obtained from this method are compared with the exact solutions and other methods (Akram and Rehman (2013), Farajeyan and Maleki (2012), Geng and Li (2009), Golbabai and Javidi (2007), He (2007), Inc and Evans (2004), Lamnii et al. (2008), Siddiqi and Akram (2007), Siddiqi et al. (2012), Siddiqi et al. (2009), Siddiqi and Iftikhar (2013), Siddiqi and Twizell (1996), Siddiqi and Twizell (1998), Torvattanabun and Koonprasert (2010), and Kasi Viswanadham and Raju (2012)) revealing that the present method is more accurate.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 427521, 12 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511870

Digital Object Identifier
doi:10.1155/2013/427521

Mathematical Reviews number (MathSciNet)
MR3049378

Zentralblatt MATH identifier
06209294

Citation

Siddiqi, Shahid S.; Iftikhar, Muzammal. Numerical Solution of Higher Order Boundary Value Problems. Abstr. Appl. Anal. 2013 (2013), Article ID 427521, 12 pages. doi:10.1155/2013/427521. https://projecteuclid.org/euclid.aaa/1393511870


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