International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2569

Full Length Research Paper

Solution of sixth-order boundary-value problems by collocation method using Haar wavelets

Fazal-i-Haq1*, Arshed Ali2,4 and Iltaf Hussain3
1Department of Mathematics, Statistics and Computer Science, Khyber Pakhtunkhwa Agricultural University, Peshawar, Pakistan. 2Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan. 3Department of Basic Sciences and Islamiat, University of Engineering and Technology Peshawar (Mardan Campus), Khyber Pakhtunkhwa, Pakistan. 4Department of Mathematics, Bacha Khan University, Charsadda, Pakistan.
Email: [email protected]

  •  Accepted: 13 July 2011
  •  Published: 16 November 2012

Abstract

A new method based on uniform Haar wavelets is proposed for the numerical solution of sixth-order two-point boundary value problems (BVPs) in ordinary differential equations. Numerical examples are given to illustrate the practical usefulness of present approach. Accuracy and efficiency of the suggested method is established through comparison with the existing spline based technique and variational iteration method. Haar wavelets have useful properties like simple applicability, orthogonality and compact support. In comparison the beauty of other wavelets like Walsh wavelet functions and wavelets of high order spline basis is overshadowed by computational cost of the algorithm. In the case of Haar wavelets, more accurate solutions can be obtained by increasing the level in the Haar wavelet. The main advantage of this method is its efficiency and simple applicability.

 

Key words: Sixth-order boundary-value problem (BVP), Haar wavelets, ordinary differential equations, dynamo action.