Abstract: Publication year: 2018Source: American Journal of Computational and Applied Mathematics , Volume 8, Number 3Masoud SaraviUsually the methods based on Taylor expansion series for have better convergence [1]. But, nearly, all of them contain one or more derivatives of . The purpose of this paper is to introduce a technique to obtain free from derivatives which works better than methods others that been considered in most text book for solving nonlinear equations by providing some numerical examples.

Abstract: Publication year: 2018Source: American Journal of Computational and Applied Mathematics , Volume 8, Number 2J. SundayOne of the most efficient ways to model the propagation of epistemic uncertainties (in dynamical environments/systems) encountered in applied sciences, engineering and even social sciences is to employ Fuzzy Differential Equations (FDEs). The FDEs are special type of Interval Differential Equations (IDEs). The IDEs are differential equations used to handle interval uncertainty that appears in many mathematical or computer models. The concept of generalized Hukuhara (gH) differentiability shall be applied in analyzing such equations. We further apply a highly efficient computational method to approximate the solution of some modeled FDEs. The results obtained clearly showed that the method adopted in the research is efficient and computationally reliable.

Abstract: Publication year: 2018Source: American Journal of Computational and Applied Mathematics , Volume 8, Number 2R. ThukralA new secant-type method for finding zeros of nonlinear equations is presented. In terms of computational cost the new iterative method requires two evaluations of functions per iteration. It is shown and proved that the new method has a convergence of order . We examine the effectiveness of the new method by approximating the simple root of several nonlinear equations. Numerical examples are given to demonstrate exceptional convergence speed of the proposed method. It is observed that our proposed method is competitive with other similar robust methods and very effective in high precision computations.

Abstract: Publication year: 2018Source: American Journal of Computational and Applied Mathematics , Volume 8, Number 2A. J. SousIn the present work, we give a numerical solution of the radial Schrödinger equation for new four-parameter radial non-conventional potential, which was introduced by Alhaidari. In our calculations, we applied the asymptotic iteration method (AIM) to calculate the eigenvalues of the potential for arbitrary parameters and any ℓ state. It is found that this method gives highly accurate results that compares favorably with other. Moreover, some new results were presented in this paper.

Abstract: Publication year: 2018Source: American Journal of Computational and Applied Mathematics , Volume 8, Number 1Shuker Mahmood Khalil, Mayadah Abd UlrazaqIn this work, we introduce new category of soft topological space is called soft closed topological space, also we study in details the properties of soft closed space and its relation with soft second-countable space, we state that every soft second-countable space is soft closed but the converse is not true in general, also we describe its relation with soft Lindelof space, soft compact space, and soft absolutely closed space.

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.