The Variational Approach Coupled with an Ancient Chinese Mathematical Method to the Relativistic Oscillator

Zhou, Lin; He, Ji‐Huan

doi:10.3390/mca15050930

Search citation statements

Order By: Relevance

Paper Sections

Select...

A New Algorithm Based On An Ancient Chinese Methods1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2012

2016

Publication Types

Select...

Article4

Relationship

Self Cite0

Independent4

Authors

Journals

Cited by 4 publications

(2 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…e ancient Chinese mathematics revives modern applications [1][2][3][4][5][6][7][8]; hereby, we show that He's max-min approach [1,[9][10][11] is also very effective for nonlinear oscillators with discontinuous terms.…”

mentioning

confidence: 83%

He's Max-Min Approach to a Nonlinear Oscillator with Discontinuous Terms

Zhang

Xie

2013

Abstract and Applied Analysis

View full text Add to dashboard Cite

show abstract

mentioning

confidence: 83%

He's Max-Min Approach to a Nonlinear Oscillator with Discontinuous Terms

Zhang

Xie

2013

Abstract and Applied Analysis

View full text Add to dashboard Cite

show abstract

“…Some ancient Chinese algorithms have been becoming hot topics in solving numerically nonlinear equations (Zhang and Xie, 2013; He et al , 2012; Zhang and Qin, 2011; Xu, 2011; He and Yang, 2010; Zhou and He, 2010; Zhong, 2009). According to an ancient Chinese algorithm, Ying Buzu Shu, choosing two initial guesses x 1 and x 2 , we can predict a more accurate solution, which is (He, 2002, 2004): …”

Section: A New Algorithm Based On An Ancient Chinese Methodsmentioning

confidence: 99%

An introduction to an ancient Chinese algorithm and its modification

He¹

2016

HFF

View full text Add to dashboard Cite

Purpose Every student knows Newton’s iteration method from a textbook, which is widely used in numerical simulation, what few may know is that its ancient Chinese partner, Ying Buzu Shu, in about second century BC has much advantages over Newton’s method. The purpose of this paper is to introduce the ancient Chinese algorithm and its modifications for numerical simulation. Design/methodology/approach An example is given to show that the ancient Chinese algorithm is insensitive to initial guess, while a fast convergence rate is predicted. Findings Two new algorithms, which are suitable for numerical simulation, are introduced by absorbing the advantages of the Newton iteration method and the ancient Chinese algorithm. Research limitations/implications This paper focuses on a single algebraic equation; however, it is easy to extend the theory to algebraic systems. Practical implications The Newton iteration method can be updated in numerical simulation. Originality/value The ancient Chinese algorithm is elucidated to have modern applications in various numerical methods.

show abstract