scholarly journals Development and application of numerical methods for solving tasks in unlimited regions based on the third Green formula

2018 ◽  
pp. 1-24 ◽  
Author(s):  
Mikhail Pavlovich Galanin ◽  
Dmitriy Leonidovich Sorokin
Keyword(s):  
Numerical Methods ◽  
Green Formula ◽  
The Third

scholarly journals Convergence Research of Numerical Methods for Solving Problems With Mixed Type Operator in an Unlimited Area

2020 ◽  
Vol 23 (4) ◽  
pp. 656-665
Author(s):  
Mikhail Pavlovich Galanin ◽  
Dmitry Leonidovich Sorokin
Keyword(s):  
Numerical Methods ◽  
Unbounded Domain ◽  
Elliptic Equations ◽  
Mixed Type ◽  
Computational Experiments ◽  
Type Operator ◽  
Green Formula ◽  
The Third ◽  
New Methods

Methods for solving problems of elliptic equations, based on the third Green formula, was analyzed. New methods for solving a problem with a mixed-type operator in an unbounded domain are proposed. On the basis of the proposed methods, programs for solving problems with a mixed type operator have been created. The results of computational experiments, showing the correctness of the application of methods, are presented.

Tethering in pastures new

2018 ◽  
Vol 102 (554) ◽  
pp. 233-245
Author(s):  
John D. Mahony
Keyword(s):  
Numerical Methods ◽  
Three Dimensional ◽  
The Other ◽  
List Type ◽  
Type Number ◽  
The Third ◽  
Slip Rings

In a recent and illuminating article that provided much food for thought [1], the problem of tethering a goat at the edge of a circular pasture so as to restrict its attentions to only one half of the grazing supply was elegantly addressed and developed further to embrace the corresponding three-dimensional scenario involving a bird. The exercises resulted in mathematical formulations that required the use of numerical methods to extract practical results. Following the article, various questions and different scenarios sprang to my mind. The following poser perhaps best illustrates one of these, and it is the purpose of this Article to address this particular conundrum:A grazier has three troublesome beasts that are water averse, eat grass and who will, given half a chance, eat one another also in some fashion. The first will eat the other two and the second will eat only the third, which eats just grass. Having stabled and fed them in separate stalls during the winter months he plans to release them in the spring to an arbitrarily elliptic shaped pasture up to the water's edge in the middle of a lake. He has at his disposal: (1)A drum of tethering rope from which he can cut just once any required length, TBD (To Be Determined).(2)Slip rings and two tethering pegs that can be positioned only on the pasture boundary (i.e. at the water's edge).

Numerical Methods I

2021 ◽  
Author(s):  
Boris Obsieger
Keyword(s):  
Numerical Methods ◽  
Direct Methods ◽  
Historical Background ◽  
Random Errors ◽  
Practical Application ◽  
Fourth Degree ◽  
Numerical Errors ◽  
The Third ◽  
Numeral Systems ◽  
The Given

Textbook, established at several universities. Second edition. *** Written primarily for students at technical studies. Valuable handbook for engineers, PhD students and scientists. *** Published in several variants. *** Seven chapters. In the first chapter, a historical background and basic properties of various numeral systems, as well as conversion of numbers from one system to another are briefly explained. In the second chapter, numbers in digital computers, namely integers and floating point numbers are described. This helps the reader to choose precision and range limits of stored numbers. The third chapter explains constant variables and related numerical errors, including error propagation and algorithm instability. The fourth and fifth chapters explain random variables and related random errors, uncertainty, confidence level, as well as propagation of random errors. Various types of regression analyses of experimental data are described in the sixth chapter. Direct methods for finding roots of the third and fourth degree polynomials are described in the seventh chapter, followed by general iterative methods for polynomials of any degree. *** Why the presented topics are so important? Simply, they are common to all numerical methods. *** Practical application is supported by 84 examples and 17 algorithms. For reasons of simplicity, algorithms are written in pseudo-code, so they can easily be implemented in any computer program. Finally, the given text with 98 figures and 52 tables represents a valuable background for understanding, applying and developing various numerical analyses.

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