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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Bibliographic Details
Main Authors: Xiaofeng Wang, Qiannan Fan
Format: Article
Language:English
Published: MDPI AG 2020-04-01
Series:Mathematics
Subjects:
self-accelerating type method
iterative method
variable parameter
root-finding
Online Access:https://www.mdpi.com/2227-7390/8/4/540
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spelling doaj-2815ae66b6484b92bbbfd313e9ad95e92020-11-25T02:51:09ZengMDPI AGMathematics2227-73902020-04-01854054010.3390/math8040540A Modified Ren’s Method with Memory Using a Simple Self-Accelerating ParameterXiaofeng Wang0Qiannan Fan1School of Mathematics and Physics, Bohai University, Jinzhou 121000, ChinaSchool of Mathematics and Physics, Bohai University, Jinzhou 121000, ChinaIn 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mo>+</mo> <msqrt> <mn>6</mn> </msqrt> <mo>≈</mo> <mrow> <mn>4.4495</mn> </mrow> </mrow> </semantics> </math> </inline-formula>. Numerical experiments are made to show the performance of the new method, which supports the theoretical results.https://www.mdpi.com/2227-7390/8/4/540self-accelerating type methoditerative methodvariable parameterroot-finding
collection DOAJ
language English
format Article
sources DOAJ
author Xiaofeng Wang
Qiannan Fan
spellingShingle Xiaofeng Wang
Qiannan Fan
A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter
Mathematics
self-accelerating type method
iterative method
variable parameter
root-finding
author_facet Xiaofeng Wang
Qiannan Fan
author_sort Xiaofeng Wang
title A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter
title_short A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter
title_full A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter
title_fullStr A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter
title_full_unstemmed A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter
title_sort modified ren’s method with memory using a simple self-accelerating parameter
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2020-04-01
description 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mo>+</mo> <msqrt> <mn>6</mn> </msqrt> <mo>≈</mo> <mrow> <mn>4.4495</mn> </mrow> </mrow> </semantics> </math> </inline-formula>. Numerical experiments are made to show the performance of the new method, which supports the theoretical results.
topic self-accelerating type method
iterative method
variable parameter
root-finding
url https://www.mdpi.com/2227-7390/8/4/540
work_keys_str_mv AT xiaofengwang amodifiedrensmethodwithmemoryusingasimpleselfacceleratingparameter
AT qiannanfan amodifiedrensmethodwithmemoryusingasimpleselfacceleratingparameter
AT xiaofengwang modifiedrensmethodwithmemoryusingasimpleselfacceleratingparameter
AT qiannanfan modifiedrensmethodwithmemoryusingasimpleselfacceleratingparameter
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