Another Newton-type method with (k+2) order convergence for solving quadratic equations

In this paper we define another Newton-type method for finding simple root of quadratic equations. It is proved that the new one-point method has the convergence order of k  2 requiring only three function evaluations per full iteration,where k is the number of terms in the generating series. The Kung and Traub conjecture states that the multipoint iteration methods, without memory based on n function evaluations, could achieve maximum convergence order 1 2nï€ ­but, the new method produces convergence order of nine, which is better than the expected maximum convergence order. Finally, we have demonstrated that our present method is very competitive with the similar methods

New variants of the Schroder method for finding zeros of nonlinear equations having unknown multiplicity

There are two aims of this paper, firstly, we define new variants of the Schroder method for finding zeros of nonlinear equations having unknown multiplicity and secondly, we introduce a new formula for approximating multiplicity m. Using the new formula, the five particular well-established methods are identical to the classical Schroder method. In terms of computational cost the new iterative method requires three evaluations of functions per iteration. It is proved that the each of the methods has a convergence of order two. Numerical examples are given to demonstrate the performance of the methods with and without multiplicity m

Introduction to a family of Thukral k-order method for finding multiple zeros of nonlinear equations

A new one-point k-order iterative method for finding zeros of nonlinear equations having unknown multiplicity is introduced.  In terms of computational cost the new iterative method requires k+1 evaluations of functions per iteration.  It is shown that the new iterative method has a convergence of order k

KINEMATIC ANALYSIS OF SURFACE AND UNDERWATER FIN-SWIMMING

The aim of the study was to perform a comparative kinematic analysis of surface and underwater fin-swimming. Results of the experiments were obtained in terms of motion as well as maximum and minimum differences between the technique of surface and underwater fin-swimming

A class of optimal eighth-order derivative-free methods for solving the Danchick-Gauss problem

A derivative-free optimal eighth-order family of iterative methods for solving nonlinear equations is constructed using weight functions approach with divided first order differences. Its performance, along with several other derivative-free methods, is studied on the specific problem of Danchick's reformulation of Gauss' method of preliminary orbit determination. Numerical experiments show that such derivative-free, high-order methods offer significant advantages over both, the classical and Danchick's Newton approach. (C) 2014 Elsevier Inc. All rights reserved.This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02.Andreu Estellés, C.; Cambil Teba, N.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2014). A class of optimal eighth-order derivative-free methods for solving the Danchick-Gauss problem. Applied Mathematics and Computation. 232:237-246. https://doi.org/10.1016/j.amc.2014.01.056S23724623

Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation

In this work we show a general procedure to obtain optimal derivative free iterative methods for nonlinear equations f (x) = 0, applying polynomial interpolation to a generic optimal derivative free iterative method of lower order. Let us consider an optimal method of order q = 2(n-1), v = phi(n)(x), that uses n functional evaluations. Performing a Newton step w = v - f(v)/f'(v) one obtains a method of order 2(n), that is not optimal because it introduces two new functional evaluations. Instead, we approximate the derivative by using a polynomial of degree n that interpolates n+1 already known functional values and keeps the order 2(n). We have applied this idea to Steffensen's method, obtaining a family of optimal derivative free iterative methods of arbitrary high order. We provide different numerical tests, that confirm the theoretical results and compare the new family with other well known family of similar characteristics. (C) 2012 Elsevier Ltd. All rights reserved.This research was supported by Ministerio de Ciencia e Innovacion MTM2011-28636-C02-02 and by Vicerrectorado de Investigacion. Universitat Politecnica de Valencia PAID-06-2010-2285.Cordero Barbero, A.; Hueso Pagoaga, JL.; Martínez Molada, E.; Torregrosa Sánchez, JR. (2013). Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation. Mathematical and Computer Modelling. 57(7-8):1950-1956. https://doi.org/10.1016/j.mcm.2012.01.012S19501956577-

An Ill Wind? Climate Change, Migration, and Health

Background: Climate change is projected to cause substantial increases in population movement in coming decades. Previous research has considered the likely causal influences and magnitude of such movements and the risks to national and international security. There has been little research on the consequences of climate-related migration and the health of people who move

Optimal iterative methods for finding multiple roots of nonlinear equations using free parameters

[EN] In this paper, we propose a family of optimal eighth order convergent iterative methods for multiple roots with known multiplicity with the introduction of two free parameters and three univariate weight functions. Also numerical experiments have applied to a number of academical test functions and chemical problems for different special schemes from this family that satisfies the conditions given in convergence result.This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C02-2-P and Generalitat Valenciana PROMETEO/2016/089.Zafar, F.; Cordero Barbero, A.; Quratulain, R.; Torregrosa Sánchez, JR. (2018). Optimal iterative methods for finding multiple roots of nonlinear equations using free parameters. Journal of Mathematical Chemistry. 56(7):1884-1901. https://doi.org/10.1007/s10910-017-0813-1S18841901567R. Behl, A. Cordero, S.S. Motsa, J.R. Torregrosa, On developing fourth-order optimal families of methods for multiple roots and their dynamics. Appl. Math. Comput. 265(15), 520–532 (2015)R. Behl, A. Cordero, S.S. Motsa, J.R. Torregrosa, V. Kanwar, An optimal fourth-order family of methods for multiple roots and its dynamics. Numer. Algor. 71(4), 775–796 (2016)R. Behl, A. Cordero, S.S. Motsa, J.R. Torregrosa, An eighth-order family of optimal multiple root finders and its dynamics. Numer. Algor. (2017). doi: 10.1007/s11075-017-0361-6F.I. Chicharro, A. Cordero, J. R. Torregrosa, Drawing dynamical and parameters planes of iterative families and methods. Sci. World J. ID 780153 (2013)A. Constantinides, N. Mostoufi, Numerical Methods for Chemical Engineers with MATLAB Applications (Prentice Hall PTR, New Jersey, 1999)J.M. Douglas, Process Dynamics and Control, vol. 2 (Prentice Hall, Englewood Cliffs, 1972)Y.H. Geum, Y.I. Kim, B. Neta, A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics. Appl. Math. Comput. 270, 387–400 (2015)Y.H. Geum, Y.I. Kim, B. Neta, A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points. Appl. Math. Comput. 283, 120–140 (2016)J.L. Hueso, E. Martınez, C. Teruel, Determination of multiple roots of nonlinear equations and applications. J. Math. Chem. 53, 880–892 (2015)L.O. Jay, A note on Q-order of convergence. BIT Numer. Math. 41, 422–429 (2001)S. Li, X. Liao, L. Cheng, A new fourth-order iterative method for finding multiple roots of nonlinear equations. Appl. Math. Comput. 215, 1288–1292 (2009)S.G. Li, L.Z. Cheng, B. Neta, Some fourth-order nonlinear solvers with closed formulae for multiple roots. Comput. Math. Appl. 59, 126–135 (2010)B. Liu, X. Zhou, A new family of fourth-order methods for multiple roots of nonlinear equations. Nonlinear Anal. Model. Control 18(2), 143–152 (2013)M. Shacham, Numerical solution of constrained nonlinear algebraic equations. Int. J. Numer. Method Eng. 23, 1455–1481 (1986)M. Sharifi, D.K.R. Babajee, F. Soleymani, Finding the solution of nonlinear equations by a class of optimal methods. Comput. Math. Appl. 63, 764–774 (2012)J.R. Sharma, R. Sharma, Modified Jarratt method for computing multiple roots. Appl. Math. Comput. 217, 878–881 (2010)F. Soleymani, D.K.R. Babajee, T. Lofti, On a numerical technique forfinding multiple zeros and its dynamic. J. Egypt. Math. Soc. 21, 346–353 (2013)F. Soleymani, D.K.R. Babajee, Computing multiple zeros using a class of quartically convergent methods. Alex. Eng. J. 52, 531–541 (2013)R. Thukral, A new family of fourth-order iterative methods for solving nonlinear equations with multiple roots. J. Numer. Math. Stoch. 6(1), 37–44 (2014)R. Thukral, Introduction to higher-order iterative methods for finding multiple roots of nonlinear equations. J. Math. Article ID 404635 (2013)X. Zhou, X. Chen, Y. Song, Constructing higher-order methods for obtaining the muliplte roots of nonlinear equations. J. Comput. Math. Appl. 235, 4199–4206 (2011)X. Zhou, X. Chen, Y. Song, Families of third and fourth order methods for multiple roots of nonlinear equations. Appl. Math. Comput. 219, 6030–6038 (2013

Plant Species Diversity along an Altitudinal Gradient of Bhabha Valley in Western Himalaya

The present study highlights the rich species diversity of higher plants in the Bhabha Valley of western Himalaya in India. The analysis of species diversity revealed that a total of 313 species of higher plants inhabit the valley with a characteristic of moist alpine shrub vegetation. The herbaceous life forms dominate and increase with increasing altitude. The major representations are from the families Asteraceae, Rosaceae, Lamiaceae and Poaceae, suggesting thereby the alpine meadow nature of the study area. The effect of altitude on species diversity displays a hump-shaped curve which may be attributed to increase in habitat diversity at the median ranges and relatively less habitat diversity at higher altitudes. The anthropogenic pressure at lower altitudes results in low plant diversity towards the bottom of the valley with most of the species being exotic in nature. Though the plant diversity is less at higher altitudinal ranges, the uniqueness is relatively high with high species replacement rates. More than 90 % of variability in the species diversity could be explained using appropriate quantitative and statistical analysis along the altitudinal gradient. The valley harbours 18 threatened and 41 endemic species, most of which occur at higher altitudinal gradients due to habitat specificit