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

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.

KEYWORDS:

• Multi-point chebyshev-like methods
• R-order of convergence
• non-linear equation in banach space
• generalized continuity condition

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65J15
• 65H10

Disclosure statement

No potential conflict of interest was reported by the authors.