A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter

A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter

In this paper, a self-accelerating type method is proposed for solving nonlinear equations, which is a modified Ren’s method. A simple way is applied to construct a variable self-accelerating parameter of the new method, which does not increase any computational costs. The highest convergence order...

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Veröffentlicht in:Mathematics (Basel) 2020-04, Vol.8 (4), p.540
Hauptverfasser: Wang, Xiaofeng, Fan, Qiannan
Format: Artikel
Sprache:eng
Schlagworte:
Efficiency
iterative method
Iterative methods
Mathematics
Methods
Nonlinear equations
Parameter modification
root-finding
self-accelerating type method
variable parameter
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Zusammenfassung:In this paper, a self-accelerating type method is proposed for solving nonlinear equations, which is a modified Ren’s method. A simple way is applied to construct a variable self-accelerating parameter of the new method, which does not increase any computational costs. The highest convergence order of new method is 2 + 6 ≈ 4.4495 . Numerical experiments are made to show the performance of the new method, which supports the theoretical results.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8040540