Comparative Study of Various Iterative Numerical Methods for Computation of Approximate Root of the Polynomials

The aim of this article is to present a brief review and a numerical comparison of iterative methods applied to solve the polynomial equations with real coefficients. In this paper, four numerical methods are compared, namely: Horner’s method, Synthetic division with Chebyshev method (Proposed Method), Synthetic division with Modified Newton Raphson method and Birge-Vieta method which will helpful to the readers to understand the importance and usefulness of these methods.

Least-Squares Chebyshev Method for Solving Fractional Integro-diffrential Equations

The main purpose of this study gears towards finding numerical solution to fractional integro-differential equations. The technique involves the application of caputo properties and Chebyshev polynomials to reduce the problem to system of linear algebraic equations and then solved using MAPLE 18. To demonstrate the accuracy and applicability of the presented method some numerical examples are given. Numerical results show that the method is easy to implement and compares favorably with the exact results. The graphical solution of the method is displayed.

Identification and Classification of Pathogenic Bacteria Using the K-Nearest Neighbor Method

Bacteria are a group of living things or organisms that do not have a core covering. In the grouping, some bacteria are pathogenic. With a microscopic size, many pathogenic bacteria are found around and spread through the food eaten or by touching objects around them, then cause diseases such as diarrhea, vomiting, and others. As a more effective effort to help the government and society prevent disease caused by pathogenic bacteria, a system for the identification and classification of pathogenic bacteria K-Nearest Neighbor was created. This system uses a biological microscope that is attached to a webcam camera above the ocular lens as a tool to see bacterial objects and assist in bacterial capture. Rough player rotates automatically (auto-focus) in image capture. In the process of classification and identifying bacteria, the K-Nearest Neighbor method is used, which is a method with the calculation of the nearest neighbor or calculation based on the level of similarity to the dataset. In this study, the bacteria vibrio chlorae, staphylococcus aereus, and streptococcus m. with the highest accuracy is the K = 9 value of 97.77% using the Chebyshev method.

Thermal stress analysis of functionally graded solid and hollow thick-walled structures with heat generation

Purpose This paper aims to present thermal and mechanical stresses in solid and hollow thick-walled cylinders and spheres made of functionally graded materials (FGMs) under the effect of heat generation. Design/methodology/approach Constant internal temperature and convective external conditions in hollow bodies along with internal heat generation with a combination of outer convective conditions in solid bodies are investigated individually. The effect of the heat convection coefficient on solid bodies is additionally discussed. The variation of the FGM properties in the radial direction is adapted to the Mori–Tanaka homogenization schemes, which produces irregular and two-point linear boundary value problems that are numerically solved by the pseudospectral Chebyshev method. Findings It has been shown that the selection of the mixtures of FGMs has to be made correctly to keep the thermal and mechanical loads acting on objects at low levels. Originality/value In this study, both solid and hollow functionally graded cylinders and spheres for different boundary conditions that are as their engineering applications are examined with the proposed method. The results have demonstrated that the pseudospectral Chebyshev method has high accuracy, low calculation costs and ease of application and can be easily adapted to such engineering problems.

On the Comparison of Gauss and Hybrid Methods and their Application to Calculation of Definite Integrals

As is known there is the wide class of methods for calculation of the definite integrals constructed by the well-known scientists as Newton, Gauss, Chebyshev, Cotes, Simpson, Krylov and etc. It seems that to receive a new result in this area is impossible. The aim of this work is the applied some general form of hybrid methods to computation of definite integral and compares that with the Gauss method. The generalization of the Gauss quadrature formula have been fulfilled in two directions. One of these directions is the using of the implicit methods and the other is the using of the advanced (forward-jumping) methods. Here have compared these methods by shown its advantages and disadvantages in the results of which have recommended to use the implicit method with the special structure. And also are constructed methods, which have applied to calculation of the definite integral with the symmetric bounders. As is known, one of the popular methods for calculation of the definite integrals with the symmetric bounders is the Chebyshev method. Therefore, here have defined some relations between of the above mentioned methods. For the application constructed, here methods are defined the necessary conditions for its convergence. The receive results have illustrated by calculation the values for some model integral using the methods with the degree p  8.

Family of Optimal Fourth Order Methods for Multiple Roots and their Dynamics

In this paper, we propose a family of fourth order method for solving non-linear equations with multiple roots. The method is based on the arithmetic mean of Weerakoon method and Chebyshev method for multiple roots. Some numerical examples are provided in support of the theoretical results. The numerical results obtained by the method for different values of the parameter are compared with some known methods. The dynamical behaviour of methods is discussed and basins of attraction around the multiple roots for some polynomial is shown at the end of the work.