Abstract: Publication date: Aug 2018 Source:Universal Journal of Computational Mathematics Volume 6 Number 1 N.M. Alrasheedi and I.A. Alsubiahi Solving nonlinear equations is one of the most important problems in numerical analysis, and has a wide range of application in various aspects, as well as many branches of science, engineering, physics, computing, astronomy, finance, .. . Generally, it is difficult to find the exact root of the nonlinear equations, and so iterative methods become the efficient way to obtain approximate solutions. Recently Kou et. al. presented a class of new variants of Ostrowski's method with order of convergence equals seven (OSM7) for solving simple roots of nonlinear equations proposed in [7]. Ostrowski's method (OSM7) has efficiency index equals to ∜7≈1.626, it has four functions per iteration but its order of convergence is seven that means it's not optimal method. In this paper, we have proposed new two improvements of Ostrowski's method (OSM7) to make it an optimal eight family and to increase its efficiency index. The first improvement has obtained by multiplied the third step of (OSM7) by product of two weight functions with some special conditions and the second improvement has obtained by multiplied the third step of (OSM7) by summation of two others weigh functions with special conditions, too. Using weight functions in every improvement helped us to improve the order of convergence of (OSM7) from seven to eight without changing the number of function evaluations to be an optimal family. New two optimal families have efficiency index equals to ∜8≈1.682. Some numerical examples are provided to show the good performance of the new methods. PubDate: Aug 2018

Abstract: Publication date: Aug 2018 Source:Universal Journal of Computational Mathematics Volume 6 Number 1 Ayda Valinezhad Orang and Hassan Hajimohammadi Wireless sensor networks (WSNs) consist of a number of nodes and one or two base stations (BS). Each node has limited energy. Therefore, the energy each node is very important parameter in network since accessing the nodes and re-charging them are difficult or in some cases, are impossible. Thus, the main purpose of this article is to increase the lifetime of the wireless sensor networks by finding the optimal route to send the data to the base station in order to save the energy of each node. In this paper, a hybrid clustering method called Hybrid based on Bayesian Networks (HBN) is proposed based on Bayesian network which considers the radio range of each nodes. In this algorithm, four different parameters are considered including residual energy, the distance to the base station, distance to the neighbor nodes and the radio range of the sensor nodes. According to the simulation results, this algorithm enables an increase in network lifetime in comparison to other similar algorithms. PubDate: Aug 2018