scholarly journals Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method

2021 ◽  
Vol 5 (4) ◽  
pp. 165
Author(s):  
Mohamed Abdelhakem ◽  
Toqa Alaa-Eldeen ◽  
Dumitru Baleanu ◽  
Maryam G. Alshehri ◽  
Mamdouh El-Kady
Keyword(s):  
Error Analysis ◽  
Galerkin Method ◽  
Chebyshev Polynomials ◽  
Real Life ◽  
Operational Matrices ◽  
Integer Order ◽  
First Derivative ◽  
The Core ◽  
Life Problems ◽  
Derivatives Of

An efficient technique, called pseudo-Galerkin, is performed to approximate some types of linear/nonlinear BVPs. The core of the performance process is the two well-known weighted residual methods, collocation and Galerkin. A novel basis of functions, consisting of first derivatives of Chebyshev polynomials, has been used. Consequently, new operational matrices for derivatives of any integer order have been introduced. An error analysis is performed to ensure the convergence of the presented method. In addition, the accuracy and the efficiency are verified by solving BVPs examples, including real-life problems.

scholarly journals New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
W. M. Abd-Elhameed
Keyword(s):  
Galerkin Method ◽  
Boundary Value Problems ◽  
Chebyshev Polynomials ◽  
Hypergeometric Functions ◽  
Jacobi Polynomials ◽  
Boundary Value ◽  
High Order ◽  
Sixth Order ◽  
Special Cases ◽  
Derivatives Of

This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms.

scholarly journals Local Convergence of a Family of Weighted-Newton Methods

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 103
Author(s):  
Ramandeep Behl ◽  
Ioannis K. Argyros ◽  
J.A. Machado ◽  
Ali Alshomrani
Keyword(s):  
Banach Space ◽  
Fourth Order ◽  
Local Convergence ◽  
Real Life ◽  
Newton Methods ◽  
Convergence Radius ◽  
Life Problems ◽  
Scope Of Application ◽  
Error Estimations ◽  
Derivatives Of

This article considers the fourth-order family of weighted-Newton methods. It provides the range of initial guesses that ensure the convergence. The analysis is given for Banach space-valued mappings, and the hypotheses involve the derivative of order one. The convergence radius, error estimations, and results on uniqueness also depend on this derivative. The scope of application of the method is extended, since no derivatives of higher order are required as in previous works. Finally, we demonstrate the applicability of the proposed method in real-life problems and discuss a case where previous studies cannot be adopted.

The Psychologist in the Medical School: An Example of Solving Real-Life Problems

1970 ◽  
Author(s):  
Matisyohu Weisenberg ◽  
Carl Eisdorfer ◽  
C. Richard Fletcher ◽  
Murray Wexler
Keyword(s):  
Medical School ◽  
Real Life ◽  
Life Problems

scholarly journals AnANN Model Trained on Regional Data in the Prediction of Particular Weather Conditions

2021 ◽  
Vol 11 (11) ◽  
pp. 4757
Author(s):  
Aleksandra Bączkiewicz ◽  
Jarosław Wątróbski ◽  
Wojciech Sałabun ◽  
Joanna Kołodziejczyk
Keyword(s):  
Atmospheric Pressure ◽  
Real Life ◽  
Real Data ◽  
Weather Conditions ◽  
Maximum Temperature ◽  
Air Masses ◽  
Weather Forecasts ◽  
Life Problems ◽  
The World ◽  
The City

Artificial Neural Networks (ANNs) have proven to be a powerful tool for solving a wide variety of real-life problems. The possibility of using them for forecasting phenomena occurring in nature, especially weather indicators, has been widely discussed. However, the various areas of the world differ in terms of their difficulty and ability in preparing accurate weather forecasts. Poland lies in a zone with a moderate transition climate, which is characterized by seasonality and the inflow of many types of air masses from different directions, which, combined with the compound terrain, causes climate variability and makes it difficult to accurately predict the weather. For this reason, it is necessary to adapt the model to the prediction of weather conditions and verify its effectiveness on real data. The principal aim of this study is to present the use of a regressive model based on a unidirectional multilayer neural network, also called a Multilayer Perceptron (MLP), to predict selected weather indicators for the city of Szczecin in Poland. The forecast of the model we implemented was effective in determining the daily parameters at 96% compliance with the actual measurements for the prediction of the minimum and maximum temperature for the next day and 83.27% for the prediction of atmospheric pressure.

scholarly journals Formulating Modes of Cooperative Leaning for Education for Sustainable Development

2021 ◽  
Vol 13 (6) ◽  
pp. 3465
Author(s):  
Jordi Colomer ◽  
Dolors Cañabate ◽  
Brigita Stanikūnienė ◽  
Remigijus Bubnys
Keyword(s):  
Sustainable Development ◽  
Real Life ◽  
Education For Sustainable Development ◽  
Professional Life ◽  
Global Challenges ◽  
Life Problems ◽  
The Face ◽  
Contemporary Education ◽  
The Impact

In the face of today’s global challenges, the practice and theory of contemporary education inevitably focuses on developing the competences that help individuals to find meaningfulness in their societal and professional life, to understand the impact of local actions on global processes and to enable them to solve real-life problems [...]

scholarly journals Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1242
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Eulalia Martínez ◽  
Majed Aali Alsulami
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Real Life ◽  
Multiple Roots ◽  
Computational Results ◽  
Nonlinear Functions ◽  
First Order ◽  
Life Problems ◽  
Derivative Free

There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

scholarly journals ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1456
Author(s):  
Stefka Fidanova ◽  
Krassimir Todorov Atanassov
Keyword(s):  
Decision Making ◽  
Knapsack Problem ◽  
Propositional Logic ◽  
Optimization Problems ◽  
Real Life ◽  
Combinatorial Optimization Problems ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Multiple Constraint

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the nature, when they look for a food. One of the algorithm parameters is called pheromone, and it is updated every iteration according quality of the achieved solutions. The intuitionistic fuzzy (propositional) logic was introduced as an extension of Zadeh’s fuzzy logic. In it, each proposition is estimated by two values: degree of validity and degree of non-validity. In this paper, we propose two variants of intuitionistic fuzzy pheromone updating. We apply our ideas on Multiple-Constraint Knapsack Problem (MKP) and compare achieved results with traditional ACO.

scholarly journals Calculators as Facilitators of Understanding Computational and Mathematical Contexts

2019 ◽  
Vol 1 (1) ◽  
pp. 177-183
Author(s):  
Jan Guncaga ◽  
Lilla Korenova ◽  
Jozef Hvorecky
Keyword(s):  
Soft Skills ◽  
Real Life ◽  
Theoretical Background ◽  
Learning Processes ◽  
Complex Phenomenon ◽  
Learning To Learn ◽  
Life Problems ◽  
The Subject ◽  
The Relationship

AbstractLearning is a complex phenomenon. Contemporary theories of education underline active participation of learners in their learning processes. One of the key arguments supporting this approach is the learner’s simultaneous and unconscious development of their ability of “learning to learn”. This ability belongs to the soft skills highly valued by employers today.For Mathematics Education, it means that teachers have to go beyond making calculations and memorizing formulas. We have to teach the subject in its social context. When the students start understanding the relationship between real-life problems and the role of numbers and formulas for their solutions, their learning becomes a part of their tacit knowledge. Below we explain the theoretical background of our approach and provide examples of such activities.

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