An Efficient Iterative Scheme Using Family of Chebyshev’s Operations

Seyed Hossein Mahdavi and Hashim Abdul Razak

Mathematical Problems in Engineering, 2015, vol. 2015, 1-10

Abstract:

This paper presents an efficient iterative method originated from the family of Chebyshev’s operations for the solution of nonlinear problems. For this aim, the product operation matrix of integration is presented, and therefore the operation of derivative is developed by using Chebyshev wavelet functions of the first and second kind, initially. Later, Chebyshev’s iterative method is improved by approximation of the first and second derivatives. The analysis of convergence demonstrates that the method is at least fourth-order convergent. The effectiveness of the proposed scheme is numerically and practically evaluated. It is concluded that it requires the less number of iterations and lies on the best performance of the proposed method, especially for highly varying nonlinear problems.

Date: 2015
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2015/205295.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2015/205295.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:205295

DOI: 10.1155/2015/205295

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().