An efficient iterative scheme using family of Chebyshev's operations
type: Item
instance of: scholarly article
title: An efficient iterative scheme using family of Chebyshev's operations
zbMATH Open document ID: 1394.65177
DOI: 10.1155/2015/205295
author: Seyed Hossein Mahdavi
author: Hashim Abdul Razak
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 6925756
Wikidata QID: Q59117595
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/205295
OpenAlex ID: W2006254908
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description: scientific article; zbMATH DE number 6925756