scholarly journals New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permittingf′(xn)=0

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Ramandeep Behl ◽  
V. Kanwar
Keyword(s):  
Higher Order ◽  
The Other ◽  
Robust Methods ◽  
Challenging Problem ◽  
Order Convergence ◽  
Dynamical Study ◽  
Globally Convergent ◽  
Special Cases ◽  
Globally Convergent Methods ◽  
Ostrowski’S Method

Construction of higher-order optimal and globally convergent methods for computing simple roots of nonlinear equations is an earliest and challenging problem in numerical analysis. Therefore, the aim of this paper is to present optimal and globally convergent families of King's method and Ostrowski's method having biquadratic and eight-order convergence, respectively, permittingf′(x)=0in the vicinity of the required root. Fourth-order King's family and Ostrowski's method can be seen as special cases of our proposed scheme. All the methods considered here are found to be more effective to the similar robust methods available in the literature. In their dynamical study, it has been observed that the proposed methods have equal or better stability and robustness as compared to the other methods.

scholarly journals Efficient Three-Step Class of Eighth-Order Multiple Root Solvers and Their Dynamics

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 837
Author(s):  
R. A. Alharbey ◽  
Munish Kansal ◽  
Ramandeep Behl ◽  
J. A. Tenreiro Machado
Keyword(s):  
General Class ◽  
Real Life ◽  
Multiple Root ◽  
Order Convergence ◽  
Eighth Order ◽  
Dynamical Study ◽  
New Methods ◽  
Life Problems ◽  
Special Cases ◽  
New Strategy

This article proposes a wide general class of optimal eighth-order techniques for approximating multiple zeros of scalar nonlinear equations. The new strategy adopts a weight function with an approach involving the function-to-function ratio. An extensive convergence analysis is performed for the eighth-order convergence of the algorithm. It is verified that some of the existing techniques are special cases of the new scheme. The algorithms are tested in several real-life problems to check their accuracy and applicability. The results of the dynamical study confirm that the new methods are more stable and accurate than the existing schemes.

scholarly journals Some Real-Life Applications of a Newly Designed Algorithm for Nonlinear Equations and Its Dynamics via Computer Tools

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Amir Naseem ◽  
M. A. Rehman ◽  
Jihad Younis
Keyword(s):  
Fourth Order ◽  
Real Life ◽  
The Other ◽  
Complex Polynomials ◽  
Order Convergence ◽  
Computer Tools ◽  
Root Finding ◽  
Derivative Free ◽  
Engineering Problems ◽  
Ostrowski’S Method

In this article, we design a novel fourth-order and derivative free root-finding algorithm. We construct this algorithm by applying the finite difference scheme on the well-known Ostrowski’s method. The convergence analysis shows that the newly designed algorithm possesses fourth-order convergence. To demonstrate the applicability of the designed algorithm, we consider five real-life engineering problems in the form of nonlinear scalar functions and then solve them via computer tools. The numerical results show that the new algorithm outperforms the other fourth-order comparable algorithms in the literature in terms of performance, applicability, and efficiency. Finally, we present the dynamics of the designed algorithm via computer tools by examining certain complex polynomials that depict the convergence and other graphical features of the designed algorithm.

scholarly journals HIGHER-ORDER FAMILIES OF MULTIPLE ROOT FINDING METHODS SUITABLE FOR NON-CONVERGENT CASES AND THEIR DYNAMICS

2019 ◽  
Vol 24 (3) ◽  
pp. 422-444 ◽  
Author(s):  
Ramandeep Behl ◽  
Vinay Kanwar ◽  
Young Ik Kim
Keyword(s):  
Multiple Root ◽  
Multiple Roots ◽  
Robust Methods ◽  
Order Convergence ◽  
Dynamical Study ◽  
Root Finding ◽  
Modified Newton’S Method ◽  
Stable Manner ◽  
Schröder’S Method ◽  
First Time

In this paper, we present many new one-parameter families of classical Rall’s method (modified Newton’s method), Schröder’s method, Halley’s method and super-Halley method for the first time which will converge even though the guess is far away from the desired root or the derivative is small in the vicinity of the root and have the same error equations as those of their original methods respectively, for multiple roots. Further, we also propose an optimal family of iterative methods of fourth-order convergence and converging to a required root in a stable manner without divergence, oscillation or jumping problems. All the methods considered here are found to be more effective than the similar robust methods available in the literature. In their dynamical study, it has been observed that the proposed methods have equal or better stability and robustness as compared to the other methods.

scholarly journals Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 57
Author(s):  
Max-Olivier Hongler
Keyword(s):  
Burgers Equation ◽  
Higher Order ◽  
Underlying Structure ◽  
Swarm Dynamics ◽  
Special Cases ◽  
Kink Waves ◽  
Systematic Derivation ◽  
Fifth Order ◽  
Higher Order Dispersion ◽  
Order Dispersion

The concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose a systematic derivation of exact solutions for PDEs with a quadratic nonlinearity of the Burgers’ type but with arbitrary dispersive orders. As illustrations, we revisit the dissipative Kotrweg de Vries, Kuramoto-Sivashinski, and Kawahara equations (involving third, fourth, and fifth order dispersion dynamics), which in this context appear to be nothing but the simplest special cases of this infinitely rich class of nonlinear evolutions.

scholarly journals Leader-chasing behavior in negative artificial triggered lightning flashes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Fukun Wang ◽  
Jianguo Wang ◽  
Li Cai ◽  
Rui Su ◽  
Wenhan Ding ◽  
...  
Keyword(s):  
High Speed ◽  
The Other ◽  
Lightning Flash ◽  
High Speed Camera ◽  
Return Stroke ◽  
Catching Up ◽  
Special Cases ◽  
Triggered Lightning

AbstractTwo special cases of dart leader propagation were observed by the high-speed camera in the leader/return stroke sequences of a classical triggered lightning flash and an altitude-triggered lightning flash, respectively. Different from most of the subsequent return strokes preceded by only one leader, the return stroke in each case was preceded by two leaders occurring successively and competing in the same channel, which herein is named leader-chasing behavior. In one case, the polarity of the latter leader was opposite to that of the former leader and these two combined together to form a new leader, which shared the same polarity with the former leader. In the other case, the latter leader shared the same polarity with the former leader and disappeared after catching up with the former leader. The propagation of the former leader in this case seems not to be significantly influenced by the existence of the latter leader.

scholarly journals Global-Local Enhancement Network for NMF-Aware Sign Language Recognition

2021 ◽  
Vol 17 (3) ◽  
pp. 1-19
Author(s):  
Hezhen Hu ◽  
Wengang Zhou ◽  
Junfu Pu ◽  
Houqiang Li
Keyword(s):  
Sign Language ◽  
Daily Life ◽  
The Other ◽  
Challenging Problem ◽  
Language Recognition ◽  
Local Enhancement ◽  
Sign Language Recognition ◽  
Vocabulary Size ◽  
Hand Gestures ◽  
Fine Grained

Sign language recognition (SLR) is a challenging problem, involving complex manual features (i.e., hand gestures) and fine-grained non-manual features (NMFs) (i.e., facial expression, mouth shapes, etc .). Although manual features are dominant, non-manual features also play an important role in the expression of a sign word. Specifically, many sign words convey different meanings due to non-manual features, even though they share the same hand gestures. This ambiguity introduces great challenges in the recognition of sign words. To tackle the above issue, we propose a simple yet effective architecture called Global-Local Enhancement Network (GLE-Net), including two mutually promoted streams toward different crucial aspects of SLR. Of the two streams, one captures the global contextual relationship, while the other stream captures the discriminative fine-grained cues. Moreover, due to the lack of datasets explicitly focusing on this kind of feature, we introduce the first non-manual-feature-aware isolated Chinese sign language dataset (NMFs-CSL) with a total vocabulary size of 1,067 sign words in daily life. Extensive experiments on NMFs-CSL and SLR500 datasets demonstrate the effectiveness of our method.

scholarly journals Voigt Transform and Umbral Image

2020 ◽  
Vol 25 (3) ◽  
pp. 49
Author(s):  
Silvia Licciardi ◽  
Rosa Maria Pidatella ◽  
Marcello Artioli ◽  
Giuseppe Dattoli
Keyword(s):  
Spectroscopic Studies ◽  
Higher Order ◽  
Point Of View ◽  
The Other ◽  
Pivotal Role ◽  
Umbral Calculus ◽  
Laguerre Functions ◽  
Hermite And Laguerre Functions ◽  
Higher Order Functions ◽  
Voigt Function

In this paper, we show that the use of methods of an operational nature, such as umbral calculus, allows achieving a double target: on one side, the study of the Voigt function, which plays a pivotal role in spectroscopic studies and in other applications, according to a new point of view, and on the other, the introduction of a Voigt transform and its possible use. Furthermore, by the same method, we point out that the Hermite and Laguerre functions, extension of the corresponding polynomials to negative and/or real indices, can be expressed through a definition in a straightforward and unified fashion. It is illustrated how the techniques that we are going to suggest provide an easy derivation of the relevant properties along with generalizations to higher order functions.

The Circular Cylinder With a Band of Uniform Pressure on a Finite Length of the Surface

1941 ◽  
Vol 8 (3) ◽  
pp. A97-A104 ◽  
Author(s):  
M. V. Barton
Keyword(s):  
Circular Cylinder ◽  
Finite Length ◽  
Infinite Series ◽  
Fundamental Problem ◽  
The Other ◽  
Complete Picture ◽  
Uniform Pressure ◽  
Uniform Tension ◽  
Special Cases ◽  
Stress And Deformation

Abstract The solution to the fundamental problem of a cylinder with a uniform pressure over one half its length and a uniform tension on the other half is found by using the Papcovitch-Neuber solution to the general equations. In this paper, the results, given analytically in terms of infinite-series expressions, are exhibited as curves giving a complete picture of the stress and deformation. The case of a cylinder with a band of uniform pressure of any length, with the exception of very small ones, is then solved by the method of superposition. The stresses and displacements are evaluated for the special cases of a cylinder with a uniform pressure load of 1 diam and 1/2 diam in length. The problem of a cylinder heated over one half its length is solved by the same means.

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