Abstract: Publication year: 2018Source: American Journal of Computational and Applied Mathematics , Volume 8, Number 4R. ThukralThe objective of this paper is to present further development of the Simpson-type methods for finding zeros of a nonlinear equation. The new Simpson-type method is shown to converge of the order five. Per iteration the new method requires the same amount of evaluations of the function and therefore the new method has an efficiency index better than the other similar Simpson-type methods. We examine the effectiveness of the new fifth-order Simpson-type method by approximating the simple root of a given nonlinear equation. Numerical comparisons are made to show the performance of the new iterative method and thus verifies the theoretical results.

Abstract: Publication year: 2018Source: American Journal of Computational and Applied Mathematics , Volume 8, Number 4Boris MeninHeisenberg's 90-year-old tenet on uncertainties in physics asserts that, in nature, determination of the accuracy of coordinates and momentum of any material object has a fundamental limit. Besides, Planck's constant is vanishingly small, with respect to macro bodies, and hence cannot be used for practical applications. In this paper, the author proposes another novel limit, based on the concept that every model contains a certain amount of information about the object under study, and hence it must have optimal number of selected quantities. The author demonstrates how, by the usual measurements of fundamental physical constants, the proposed novel limit can be applied to estimate the permissible absolute and relative uncertainties of the metric being measured. For this, the author used the information theory for giving a theoretical explanation and for grounding of the experimental results, which determine the precision of different fundamental constants. It is shown that this new fundamental limit, characterizing the discrepancy between a model and the observed object, cannot be overcome by any improvement in measuring instruments, mathematical methods or super-powerful computers.

Abstract: Publication year: 2018Source: American Journal of Computational and Applied Mathematics , Volume 8, Number 4Pallavi P. Chopade, Prabha S. RastogiIn this paper, effective algorithms of finite difference method (FDM) and finite element method (FEM) are designed. The solution of partial differential 2-D Laplace equation in Electrostatics with Dirichlet boundary conditions is evaluated. The electric potential over the complete domain for both methods are calculated. The developed numerical solutions in MATLAB gives results much closer to exact solution when evaluated at different nodes. An error analysis is also presented where the numerical error based on the L2 norm is computed. This error reduces monotonically by reducing the mesh size.

Abstract: Publication year: 2018Source: American Journal of Computational and Applied Mathematics , Volume 8, Number 3Md. Babul Hossain, Mousumi DattaIn this paper we introduced a new method, named Elzaki Substitution Method, which is based on Elzaki transform for solving linear partial differential equations with mixed partial derivatives. This proposed method will play an important role to find exact solutions of partial differential equations involving mixed partial derivatives with less computation as compared with other methods such as Method of Separation of Variables (MSV) and Variation Iteration Method (VIM). Elzaki transforms of partial derivatives with some fundamental properties are presented in this paper. Illustrative examples are presented to demonstrate the effectiveness, efficiency and applicability of proposed method.

Abstract: Publication year: 2018Source: American Journal of Computational and Applied Mathematics , Volume 8, Number 3Karim Bouassem, Jalal Soulami, Abdellatif El Assoudi, El Hassane El YaagoubiThis paper addresses the problem of simultaneous estimation of unmeasurable states and unknown inputs (UIs) for a class of discrete-time nonlinear descriptor models (DNDMs) described by Takagi-Sugeno (T-S) structure with unmeasurable premise variables. The UIs affect both state and output of the system. The main idea of the proposed design of fuzzy unknown inputs observer (FUIO) is based on the separation between dynamic and static relations in T-S descriptor model. First, the method permitting to separate dynamic equations from static equations is developed. Next, based on the augmented fuzzy model which contains the dynamic equations and the UIs, a new FUIO design in explicit structure is given. The exponential convergence of the state estimation error is studied by using the Lyapunov theory and the stability conditions are given in terms of linear matrix inequalities (LMIs). Finally, an application to a DNDM of a single-link flexible joint robot is presented in order to illustrate the validity and applicability of the proposed method.

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.