scholarly journals A new method for solving interval and fuzzy quadratic equations of dual form

2021 ◽  
Vol 5 (2) ◽  
pp. 81-89
Author(s):  
Kamal Mamehrashi
Keyword(s):  
Numerical Method ◽  
Fuzzy Number ◽  
Quadratic Equation ◽  
New Method ◽  
Numerical Examples ◽  
Quadratic Equations ◽  
Dual Form ◽  
Interval Extension

In this paper, we present a numerical method for solving a quadratic interval equation in its dual form. The method is based on the generalized procedure of interval extension called” interval extended zero” method. It is shown that the solution of interval quadratic equation based on the proposed method may be naturally treated as a fuzzy number. An important advantage of the proposed method is that it substantially decreases the excess width defect. Several numerical examples are included to demonstrate the applicability and validity of the proposed method.

scholarly journals A New High-Order Stable Numerical Method for Matrix Inversion

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
F. Khaksar Haghani ◽  
F. Soleymani
Keyword(s):  
Iterative Method ◽  
Numerical Method ◽  
Matrix Inversion ◽  
High Order ◽  
New Method ◽  
Order Convergence ◽  
Initial Value ◽  
Numerical Examples ◽  
Stable Numerical Method

A stable numerical method is proposed for matrix inversion. The new method is accompanied by theoretical proof to illustrate twelfth-order convergence. A discussion of how to achieve the convergence using an appropriate initial value is presented. The application of the new scheme for finding Moore-Penrose inverse will also be pointed out analytically. The efficiency of the contributed iterative method is clarified on solving some numerical examples.

scholarly journals Barycentric prolate interpolation and pseudospectral differentiation

2021 ◽  
Author(s):  
Yan Tian
Keyword(s):  
Boundary Value Problem ◽  
Convergence Rates ◽  
Boundary Value ◽  
High Accuracy ◽  
Second Order ◽  
New Method ◽  
Numerical Examples ◽  
Helmholtz Problem ◽  
Collocation Scheme

AbstractIn this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

scholarly journals Numerical method of identification of an unknown source term in a heat equation

2002 ◽  
Vol 8 (2) ◽  
pp. 161-168 ◽  
Author(s):  
Afet Golayoğlu Fatullayev
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Numerical Method ◽  
Minimization Problem ◽  
Unknown Function ◽  
Source Term ◽  
Numerical Procedure ◽  
Numerical Examples ◽  
Unknown Source

A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.

An Accelerated Iterative Method with Third-Order Convergence

2012 ◽  
Vol 220-223 ◽  
pp. 2658-2661
Author(s):  
Zhong Yong Hu ◽  
Liang Fang ◽  
Lian Zhong Li
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
New Method ◽  
Order Convergence ◽  
Third Order ◽  
Numerical Examples ◽  
Modified Newton’S Method ◽  
Jarratt Method

We present a new modified Newton's method with third-order convergence and compare it with the Jarratt method, which is of fourth-order. Based on this new method, we obtain a family of Newton-type methods, which converge cubically. Numerical examples show that the presented method can compete with Newton's method and other known third-order modifications of Newton's method.

scholarly journals A New Method for the Calculation of Energy and Power Requirements of Bucket Wheel Excavators

2019 ◽  
Vol 10 (1) ◽  
pp. 15-20
Author(s):  
József András ◽  
József Kovács ◽  
Endre András ◽  
Ildikó Kertész ◽  
Ovidiu Bogdan Tomus
Keyword(s):  
Energy Consumption ◽  
Numerical Method ◽  
Horizontal Plane ◽  
Vertical Plane ◽  
New Method ◽  
Energy Requirements ◽  
Belt Conveyor ◽  
Analytical Formulas ◽  
Power And Energy ◽  
Continuous Working

Abstract The bucket wheel excavator (BWE) is a continuous working rock harvesting device which removes the rock by means of buckets armoured with teeth, mounted on the wheel and which transfers rock on a main hauling system (generally a belt conveyor). The wheel rotates in a vertical plane and swings in the horizontal plane and raised / descended in the vertical plane by a boom. In this paper we propose a graphical-numerical method in order to calculate the power and energy requirements of the main harvesting structure (the bucket wheel) of the BWE. This approach - based on virtual models of the main working units of bucket wheel excavators and their working processes - is more convenient than those based on analytical formulas and simplification hypotheses, and leads to improved operation, reduced energy consumption, increased productivity and optimal use of available actuating power.

scholarly journals Probability Transform Based on the Ordered Weighted Averaging and Entropy Difference

2020 ◽  
Vol 15 (4) ◽  
Author(s):  
Lipeng Pan ◽  
Yong Deng
Keyword(s):  
Probability Distribution ◽  
Evidence Theory ◽  
Mass Function ◽  
New Method ◽  
Weighted Averaging ◽  
Minimum Entropy ◽  
Transform Method ◽  
Numerical Examples ◽  
Ordered Weighted Averaging ◽  
Open Issue

Dempster-Shafer evidence theory can handle imprecise and unknown information, which has attracted many people. In most cases, the mass function can be translated into the probability, which is useful to expand the applications of the D-S evidence theory. However, how to reasonably transfer the mass function to the probability distribution is still an open issue. Hence, the paper proposed a new probability transform method based on the ordered weighted averaging and entropy difference. The new method calculates weights by ordered weighted averaging, and adds entropy difference as one of the measurement indicators. Then achieved the transformation of the minimum entropy difference by adjusting the parameter r of the weight function. Finally, some numerical examples are given to prove that new method is more reasonable and effective.

Solution of Basic Inventory Model in Fuzzy and Interval Environments

2017 ◽  
pp. 65-95
Author(s):  
Sankar Prasad Mondal
Keyword(s):  
Differential Equation ◽  
Fuzzy Number ◽  
Interval Number ◽  
Inventory Model ◽  
Time Dependent ◽  
Equation Approach ◽  
Numerical Examples ◽  
Fuzzy Environment

In this present paper a basic inventory model is solved in different imprecise environments. Four different cases are discussed: 1) Crisp inventory model, that is, the quantity at present and demand is crisp number; 2) Inventory model in fuzzy environment, that is, the quantity and demand both are fuzzy number; 3) Inventory model in interval environment, that is, the quantity and demand both are interval number and lastly; 4) Inventory model in time dependent fuzzy environment, that is, quantity and demand are both time dependent fuzzy number. Different numerical examples are used to illustrate the model as well as to compute the efficiency of imprecise differential equation approach to solve the model.

Small Prime Solutions of Quadratic Equations

2002 ◽  
Vol 54 (1) ◽  
pp. 71-91 ◽  
Author(s):  
Kwok-Kwong Stephen Choi ◽  
Jianya Liu
Keyword(s):  
Quadratic Equation ◽  
List Type ◽  
Quadratic Equations

AbstractLet b1,…,b5 be non-zero integers and n any integer. Suppose that b1 + … + b5 ≡ n (mod 24) and (bi, bj) = 1 for 1 ≤ i < j ≤ 5. In this paper we prove that(i)if all bj are positive and , then the quadratic equation is soluble in primes pj, and(ii)if bj are not all of the same sign, then the above quadratic equation has prime solutions satisfying .

scholarly journals A Two-Step Newton-Type Method for Solving System of Absolute Value Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Lei Shi ◽  
Javed Iqbal ◽  
Muhammad Arif ◽  
Alamgir Khan
Keyword(s):  
Newton Method ◽  
New Method ◽  
Generalized Newton Method ◽  
Absolute Value Equations ◽  
Step Method ◽  
Type Method ◽  
Numerical Examples ◽  
Absolute Value ◽  
Generalized Newton

In this paper, we suggest a Newton-type method for solving the system of absolute value equations. This new method is a two-step method with the generalized Newton method as predictor. Convergence of the proposed method is proved under some suitable conditions. At the end, we take several numerical examples to show that the new method is very effective.

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