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Original Articles

R-order of convergence for the improved multi-point Chebyshev-like methods under generalized continuity condition

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Pages 906-919 | Received 05 Mar 2017, Accepted 30 Apr 2018, Published online: 09 Apr 2019
 

ABSTRACT

In this paper, the convergence for improved multi-point Chebyshev-like methods is considered. Compared to the results of Chebyshev method with second derivative in reference [M.A. Hernández, M.A. Salanova, J. Comput. Appl. Math. 126 (2000), pp. 131–143], the R-order is maximised and the Hölder continuity condition is also relaxed. Moreover, these improved methods do not need second derivatives, when the computation of second derivative is large, these improved methods will be more efficient than Chebyshev method. Under the relaxed condition, an existence-uniqueness theorem is proved. The R-order of convergence for these improved methods is also analysed.

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

Disclosure statement

No potential conflict of interest was reported by the authors.

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