scholarly journals Some High-Order Iterative Methods for Nonlinear Models Originating from Real Life Problems

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1249
Author(s):  
Malik Zaka Ullah ◽  
Ramandeep Behl ◽  
Ioannis K. Argyros
Keyword(s):  
Nonlinear Models ◽  
Real Life ◽  
Systems Of Equations ◽  
Type Method ◽  
Life Problems ◽  
Similar Information ◽  
Large Systems ◽  
Computable Error Bounds ◽  
Theoretical Results ◽  
High Order Iterative Methods

We develop a sixth order Steffensen-type method with one parameter in order to solve systems of equations. Our study’s novelty lies in the fact that two types of local convergence are established under weak conditions, including computable error bounds and uniqueness of the results. The performance of our methods is discussed and compared to other schemes using similar information. Finally, very large systems of equations (100×100 and 200×200) are solved in order to test the theoretical results and compare them favorably to earlier works.

A class of computationally efficient Newton-like methods with frozen inverse operator for nonlinear systems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Janak Raj Sharma ◽  
Sunil Kumar
Keyword(s):  
Inverse Operator ◽  
Function Evaluation ◽  
Systems Of Nonlinear Equations ◽  
Systems Of Equations ◽  
Computationally Efficient ◽  
Additional Function ◽  
Single Use ◽  
Large Systems ◽  
The Cost ◽  
Theoretical Results

Abstract We propose a class of Newton-like methods with increasing convergence order for approximating the solutions of systems of nonlinear equations. Novelty of the methods is that in each step the order of convergence is increased by an amount of three at the cost of only one additional function evaluation. Another important feature is the single use of an inverse operator in each iteration, which makes the schemes attractive and computationally more efficient. Theoretical results regarding convergence and computational efficiency are verified through numerical examples including those arising from boundary value problems and integral equations. By way of comparison, it is shown that the present methods are more efficient than their existing counterparts, particularly when applied to solve the large systems of equations.

scholarly journals Optimization by parameters in the iterative methods for solving non-linear equations

2021 ◽  
pp. 16-22
Author(s):  
Tugal Zhanlav ◽  
Khuder Otgondorj
Keyword(s):  
Iterative Methods ◽  
Linear Equations ◽  
Real Life ◽  
Robust Methods ◽  
Life Problems ◽  
Optimal Values ◽  
Non Linear Equations ◽  
Theoretical Results ◽  
High Computational Efficiency ◽  
Methods Numerical

In this paper, we used the necessary optimality condition for parameters in a two-point iterations for solving nonlinear equations. Optimal values of these parameters fully coincide with those obtained in [6] and allow us to increase the convergence order of these iterative methods. Numerical experiments and the comparison of existing robust methods are included to confirm the theoretical results and high computational efficiency. In particular, we considered a variety of real life problems from different disciplines, e.g., Kepler’s equation of motion, Planck’s radiation law problem, in order to check the applicability and effectiveness of our proposed methods.

scholarly journals Fractal fractional derivative on chemistry kinetics hires problem

2021 ◽  
Vol 7 (1) ◽  
pp. 1155-1184
Author(s):  
Muhammad Aslam ◽  
◽  
Muhammad Farman ◽  
Hijaz Ahmad ◽  
Tuan Nguyen Gia ◽  
...  
Keyword(s):  
Chemical Kinetics ◽  
Chemical Reactions ◽  
Transfer Problem ◽  
Nonlinear Models ◽  
Real Life ◽  
Numerical Results ◽  
Actual Behavior ◽  
Caputo Fractional Derivatives ◽  
Home Heating ◽  
Life Problems

<abstract> <p>In this work, we construct the fractional order model for chemical kinetics issues utilizing novel fractal operators such as fractal fractional by using generalized Mittag-Leffler Kernel. To overcome the constraints of the traditional Riemann-Liouville and Caputo fractional derivatives, a novel notion of fractional differentiation with non-local and non-singular kernels was recently presented. Many scientific conclusions are presented in the study, and these results are supported by effective numerical results. These findings are critical for solving the nonlinear models in chemical kinetics. These concepts are very important to use for real life problems like brine tank cascade, recycled brine tank cascade, pond pollution, home heating and biomass transfer problem. Many scientific results are presented in the paper also prove these results by effective numerical results. These results are very important for solving the nonlinear model in chemistry kinetics which will be helpful to understand the chemical reactions and its actual behavior; also the observation can be developed for future kinematic chemical reactions with the help of these results.</p> </abstract>

scholarly journals Fractal fractional derivative on chemistry kinetics hires problem

2021 ◽  
Vol 7 (1) ◽  
pp. 1155-1184
Author(s):  
Muhammad Aslam ◽  
◽  
Muhammad Farman ◽  
Hijaz Ahmad ◽  
Tuan Nguyen Gia ◽  
...  
Keyword(s):  
Chemical Kinetics ◽  
Chemical Reactions ◽  
Transfer Problem ◽  
Nonlinear Models ◽  
Real Life ◽  
Numerical Results ◽  
Actual Behavior ◽  
Caputo Fractional Derivatives ◽  
Home Heating ◽  
Life Problems

<abstract> <p>In this work, we construct the fractional order model for chemical kinetics issues utilizing novel fractal operators such as fractal fractional by using generalized Mittag-Leffler Kernel. To overcome the constraints of the traditional Riemann-Liouville and Caputo fractional derivatives, a novel notion of fractional differentiation with non-local and non-singular kernels was recently presented. Many scientific conclusions are presented in the study, and these results are supported by effective numerical results. These findings are critical for solving the nonlinear models in chemical kinetics. These concepts are very important to use for real life problems like brine tank cascade, recycled brine tank cascade, pond pollution, home heating and biomass transfer problem. Many scientific results are presented in the paper also prove these results by effective numerical results. These results are very important for solving the nonlinear model in chemistry kinetics which will be helpful to understand the chemical reactions and its actual behavior; also the observation can be developed for future kinematic chemical reactions with the help of these results.</p> </abstract>

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.

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