Abstract: Publication year: 2018Source: American Journal of Computational and Applied Mathematics , Volume 8, Number 1T. Zhanlav, Kh. OtgondorjWe propose a new family of optimal eight-order methods for solving nonlinear equations. The order of convergence of proposed methods verified using sufficient convergence conditions given in [6]. Using of sufficient convergence condition allows us to develop new optimal three-point iterations. Various numerical examples are considered to check the performance and to verify the theoretical results. Numerical comparisons of proposed methods with some existing methods are made. The test results are in good accordance with our study.

Abstract: Publication year: 2018Source: American Journal of Computational and Applied Mathematics , Volume 8, Number 1Tarek H. M. Abou-El-Enien, Shereen Fathy El-FekyThis paper extended the concept of the technique for order preference by similarity to ideal solution (TOPSIS) to develop a methodology to find compromise solutions for the Multi-Level Multiple Objective Decision Making (MLMODM) Problems with fuzzy parameters in the objective functions and the right hand side of the constraints (FMLMODM) of mixed (Maximize/Minimize)-type. Anew interactive algorithm is presented for the proposed TOPSIS approach for solving these types of mathematical programming problems. Also, an illustrative numerical example is solved and compared the solution of proposed algorithm with the solution of Global Criterion (GC) method.

Abstract: Publication year: 2017Source: American Journal of Computational and Applied Mathematics , Volume 7, Number 6Ogunrinde R. B., Ayinde S. O.In this paper, we present a new numerical integration of a derived interpolating function using the Gompertz Function approach for solving first order differential equations. The new numerical integration obtained was used to solve some oscillatory and exponential problems. The effectiveness of the new Integrator was verified and the results obtained show that the Integrator is computational reliable and stable.

Abstract: Publication year: 2017Source: American Journal of Computational and Applied Mathematics , Volume 7, Number 5Maged George IskanderUsing the min-function is essential in some fuzzy programming models. It provides a wider decision space than if it is not used. In some cases, utilizing the min-function in a model within the General Algebraic Modeling System (GAMS) software may not lead to an optimal solution, since this function is not differentiable and CONOPT solver cannot always find a solution to this type of model. In this paper, the importance of using the min-function in some fuzzy programming models is presented. In addition, the smooth approximation for the min-function can be utilized when GAMS/CONOPT solver fails to reach the optimal solution of the model. A numerical example that illustrates the correctness of the proposed approach is presented.

Abstract: Publication year: 2017Source: American Journal of Computational and Applied Mathematics , Volume 7, Number 5Md. Jahangir Hossain, Md. Shah Alam, Md. Babul HossainIn this paper, we mainly present fourth order Runge-Kutta (RK4) and Butcher’s fifth order Runge-Kutta (RK5) Methods for solving second order initial value problems (IVP) for ordinary differential equations (ODE). These two proposed methods are quite proficient and practically well suited for solving engineering problems based on such problems. To obtain the accuracy of the numerical solutions for this study, we have compared the approximate solutions with the exact solutions and originate a good agreement.Numerical and graphical comparisons between fourth order Runge-Kutta method and Butcher’s fifth order Runge-Kutta method have been presented. In order to, achieve more accuracy in the solution; the step size needs to be very small. Moreover, the error terms have been analyzed of these two proposed methods for different step sizesto scrutinize supremacy. A numerical example is given to exhibit the reliability and efficiency of these two methods.

Abstract: Publication year: 2017Source: American Journal of Computational and Applied Mathematics , Volume 7, Number 5R. ThukralA new fourth-order iterative method for finding zeros of nonlinear equations is introduced. In terms of computational cost the new iterative method requires four evaluations of functions per iteration. It is shown and proved that the new method has a convergence of order four. We examine the effectiveness of the new fourth-order method by approximating the multiple roots of several nonlinear equations. Numerical examples are given to demonstrate exceptional convergence speed of the proposed method.

Abstract: Publication year: 2017Source: American Journal of Computational and Applied Mathematics , Volume 7, Number 4Abdellah Louzimi, Abdellatif El Assoudi, Jalal Soulami, El Hassane El YaagoubiThis paper investigates the problem of the fuzzy unknown inputs observer (FUIO) design for a class of discrete-time Takagi-Sugeno implicit models (DTSIMs) with unmeasurable premise variables which satisfying Lipschitz conditions. The unknown inputs (UIs) affect both state and output of the model. The idea of the proposed result is based on the separation between dynamic and static equations in the considered DTSIM. First, the method used to separate dynamic equations from static equations is developed. Next, based on the augmented system structure which contains the dynamic equations and the unknown inputs, a new observer design in explicit structure to estimate simultaneously the system state and the unknown inputs is established. The convergence of the state estimation error of the augmented system is studied by using the Lyapunov theory and the gain matrix of the FUIO is obtained by solving only one linear matrix inequality (LMI). At last, an illustrative example is given to show the effectiveness of the proposed technique.

Abstract: Publication year: 2017Source: American Journal of Computational and Applied Mathematics , Volume 7, Number 4Iwundu M. P.The bahaviours of the first compound of the hat matrix and the determinant-based loss criterion are examined for effects of a missing observation in three configurations of six-factor central composite design, varying in factorial portion. The hat matrix varies between one design configuration and another but remains unchanged within same design configuration with different defining relations. The diagonal entries of each corresponding hat matrix associated with a factorial point, an axial point and a center point respectively correspond to the losses computed using the determinant-based criterion. Loss due to missing center point in the three categories of design is very minimal when compared with loss due to either missing factorial point or missing axial point. The configuration with one-quarter fractional factorial portion attracts significantly higher losses to a missing observation of either factorial, axial or center portion when compared with either the configuration with one-half fractional factorial portion or the configuration with complete factorial portion. This is possibly because the configuration with one-quarter fractional factorial portion is near saturated. Variances associated with parameter estimates are minimum for the design category with complete factorial portion and maximum for the design category with one-quarter fractional factorial portion. Interestingly, the design category that minimizes the variances also minimizes the losses.

Abstract: Publication year: 2017Source: American Journal of Computational and Applied Mathematics , Volume 7, Number 4Mohammed Abdulrazaq Kahya, Waleed Al-Hayani, Zakariya Yahya AlgamalThe common issues of high-dimensional gene expression data are that many of genes may not be relevant to their diseases. Genes have naturally pathway structure, where the pathway contains several genes sharing a biological function. Gene selection has been proved to be an effective way to improve the result of many classification methods. It is of great interest to incorporate pathway knowledge into gene selection. In this paper, a weighted sparse support vector is proposed, with the aim of identification genes and pathways, by combining the support vector machine with the weighted L1-norm. Experimental results based on three publicly gene expression datasets show that the proposed method significantly outperforms three competitor methods in terms of classification accuracy, G-mean, and area under the curve. In addition, the results demonstrate that the top identified genes and pathways are biologically related to the cancer type. Thus, the proposed method can be useful for cancer classification using DNA gene expression data in the real clinical practice.

Abstract: Publication year: 2017Source: American Journal of Computational and Applied Mathematics , Volume 7, Number 3Michael Gr. Voskoglou, Athena PapadopoulouA Fuzzy Logic model, based on Triangular Fuzzy Numbers and on the Centre of Gravity defuzzification technique is utilized in this work for evaluating the responses of Greek secondary education teachers on questions about the character of Euclidian Geometry in the school curricula, about the difficulties that they face in communicating with their students when teaching the subject and the nature of these difficulties and about the importance of using the Euclidian Geometry in other mathematical topics taught in secondary schools. These questions were part of a written questionnaire designed by the second author of the present article for the purposes of her M.Sc. dissertation and forwarded to her colleagues for completion. Fuzzy Logic, being closer than Probability and Statistics to our natural language, enabled us here to characterize the teacher responses with linguistic expressions.