A convex combination approach for mean-based variants of Newton's method

[EN] Several authors have designed variants of Newton¿s method for solving nonlinear equations by using different means. This technique involves a symmetry in the corresponding fixed-point operator. In this paper, some known results about mean-based variants of Newton¿s method (MBN) are re-analyzed from the point of view of convex combinations. A new test is developed to study the order of convergence of general MBN. Furthermore, a generalization of the Lehmer mean is proposed and discussed. Numerical tests are provided to support the theoretical results obtained and to compare the different methods employed. Some dynamical planes of the analyzed methods on several equations are presented, revealing the great difference between the MBN when it comes to determining the set of starting points that ensure convergence and observing their symmetry in the complex plane.This research was partially funded by Spanish Ministerio de Ciencia, Innovacion y Universidades PGC2018-095896-B-C22 and by Generalitat Valenciana PROMETEO/2016/089 (Spain).Cordero Barbero, A.; Franceschi, J.; Torregrosa Sánchez, JR.; Zagati, AC. (2019). A convex combination approach for mean-based variants of Newton's method. Symmetry (Basel). 11(9):1-16. https://doi.org/10.3390/sym11091106S116119Weerakoon, S., & Fernando, T. G. I. (2000). A variant of Newton’s method with accelerated third-order convergence. Applied Mathematics Letters, 13(8), 87-93. doi:10.1016/s0893-9659(00)00100-2Özban, A. . (2004). Some new variants of Newton’s method. Applied Mathematics Letters, 17(6), 677-682. doi:10.1016/s0893-9659(04)90104-8Zhou, X. (2007). A class of Newton’s methods with third-order convergence. Applied Mathematics Letters, 20(9), 1026-1030. doi:10.1016/j.aml.2006.09.010Singh, M. K., & Singh, A. K. (2017). A New-Mean Type Variant of Newton´s Method for Simple and Multiple Roots. International Journal of Mathematics Trends and Technology, 49(3), 174-177. doi:10.14445/22315373/ijmtt-v49p524Verma, K. L. (2016). On the centroidal mean Newton’s method for simple and multiple roots of nonlinear equations. International Journal of Computing Science and Mathematics, 7(2), 126. doi:10.1504/ijcsm.2016.076403Cordero, A., & Torregrosa, J. R. (2007). Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation, 190(1), 686-698. doi:10.1016/j.amc.2007.01.062Chicharro, F. I., Cordero, A., & Torregrosa, J. R. (2013). Drawing Dynamical and Parameters Planes of Iterative Families and Methods. The Scientific World Journal, 2013, 1-11. doi:10.1155/2013/78015

Optimal leach protocol with improved bat algorithm in wireless sensor networks

© 2019, Korean Society for Internet Information. All rights reserved. A low-energy adaptive clustering hierarchy (LEACH) protocol is a low-power adaptive cluster routing protocol which was proposed by MIT’s Chandrakasan for sensor networks. In the LEACH protocol, the selection mode of cluster-head nodes is a random selection of cycles, which may result in uneven distribution of nodal energy and reduce the lifetime of the entire network. Hence, we propose a new selection method to enhance the lifetime of network, in this selection function, the energy consumed between nodes in the clusters and the power consumed by the transfer between the cluster head and the base station are considered at the same time. Meanwhile, the improved FTBA algorithm integrating the curve strategy is proposed to enhance local and global search capabilities. Then we combine the improved BA with LEACH, and use the intelligent algorithm to select the cluster head. Experiment results show that the improved BA has stronger optimization ability than other optimization algorithms, which the method we proposed (FTBA-TC-LEACH) is superior than the LEACH and LEACH with standard BA (SBA-LEACH). The FTBA-TC-LEACH can obviously reduce network energy consumption and enhance the lifetime of wireless sensor networks (WSNs)

A High Order Solution of Three Dimensional TIME Dependent Nonlinear Convective-diffusive Problem Using Modified Variational Iteration Method

In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA

A Comparative Study Between ADM and MDM for a System of Volterra Integral Equation

In this paper, a comparative study between Adomain decomposition method (ADM) and Modified decomposition method (MDM) for a system of volterra integral equation. From the illustrate examples it is observed that the exact solution is smaller in both methods, the modified decomposition method is more proficient than its traditional ones it is less complicated, needs less time to get to the solution and most importantly the exact solution is achieved in two iterations

ON THE SENSITIVITY OF THE NONLINEAR TERM IN THE OUTFLOW BOUNDARY CONDITION

This paper studies the artificial outflow boundary condition for the Navier-Stokes system. This type of condition is widely used and it is therefore very important to study its influence on a numerical solution of the corresponding boundary-value problem. We particularly focus on the role of the coefficient in front of the nonlinear term in the boundary condition on the outflow. The influence of this term is examined numerically, comparing the obtained results in a close neighbourhood of the outflow. The numerical experiment is carried out for a fluid flow through the channel with so called sudden extension. Presented numerical results are obtained by means of the OpenFOAM toolbox. They confirm that the kinetic energy of the flow in the channel can be controlled by means of the proposed boundary condition

The hub number of a fuzzy graph

In this paper, we introduced the concepts of hub number in fuzzy graph and is denoted by h(G). The hub number of fuzzy graph G is the minimum fuzzy cardinality among all minimal fuzzy hub sets . We determine the hub number h(G) for several classes of fuzzy graph and obtain Nordhaus-Gaddum type results for this parameter. Further, some bounds of h(G) are investigated. Also the relations between h(G) and other known parameters in fuzzy graphs are investigated.Publisher's Versio