1,969 research outputs found
Guaranteed error bounds for a class of Picard-Lindelöf iteration methods
No full textWe present a new version of the Picard-Lindelof method for ordinary dif- ¨
ferential equations (ODEs) supplied with guaranteed and explicitly computable upper
bounds of an approximation error. The upper bounds are based on the Ostrowski
estimates and the Banach fixed point theorem for contractive operators. The estimates
derived in the paper take into account interpolation and integration errors
and, therefore, provide objective information on the accuracy of computed approximations.peerReviewe
Domain decomposition methods for continuous casting problem
No full textAbstractSeveral numerical methods and algorithms, for solving the mathematical model of a continuous casting process, are presented, and theoretically studied, in this work. The numerical algorithms can be divided in to three different groups: the Schwarz type overlapping methods, the nonoverlapping Splitting iterative methods, and the Predictor-Corrector type nonoverlapping methods. These algorithms are all so-called parallel algorithms i.e., they are highly suitable for parallel computers. Multiplicative, additive Schwarz alternating method and two asynchronous domain decomposition methods, which appear to be a two-stage Schwarz alternating algorithms, are theoretically and numerically studied. Unique solvability of the fully implicit and semi-implicit finite difference schemes as well as monotone dependence of the solution on the right-hand side are proved. Geometric rate of convergence for the iterative methods is investigated.Splitting iterative methods for the sum of maximal monotone and single-valued monotone operators in a finite-dimensional space are studied. Convergence, rate of convergence and optimal iterative parameters are derived. A two-stage iterative method with inner iterations is analyzed in the case when both operators are linear, self-adjoint and positive definite. Several new finite-difference schemes for a nonlinear convection-diffusion problem are constructed and numerically studied. These schemes are constructed on the basis of non-overlapping domain decomposition and predictor-corrector approach. Different non-overlapping decompositions of a domain, with cross-points and angles, schemes with grid refinement in time in some subdomains, are used. All proposed algorithms are extensively numerically tested and are founded stable and accurate under natural assumptions for time and space grid steps.The advantages and disadvantages of the numerical methods are clearly seen in the numerical examples. All of the algorithms presented are quite easy and straight forward, from an implementation point of view. The speedups show that splitting iterative method can be parallelized better than multiplicative or additive Schwarz alternating method. The numerical examples show that the multidecomposition method is a very effective numerical method for solving the continuous casting problem. The idea of dividing the subdomains to smaller subdomains seems to be very beneficial and profitable. The advantages of multidecomposition methods over other methods is obvious. Multidecomposition methods are extremely quick, while being just as accurate as other methods. The numerical results for one processor seem to be very promising.Academic Dissertation to be presented with the assent of the Faculty of Science, University of Oulu, for public discussion in Kajaaninsali (Auditorium L6), Linnanmaa, on November 27th, 2004, at 12 noon.Abstract
Several numerical methods and algorithms, for solving the mathematical model of a continuous casting process, are presented, and theoretically studied, in this work. The numerical algorithms can be divided in to three different groups: the Schwarz type overlapping methods, the nonoverlapping Splitting iterative methods, and the Predictor-Corrector type nonoverlapping methods. These algorithms are all so-called parallel algorithms i.e., they are highly suitable for parallel computers.
Multiplicative, additive Schwarz alternating method and two asynchronous domain decomposition methods, which appear to be a two-stage Schwarz alternating algorithms, are theoretically and numerically studied. Unique solvability of the fully implicit and semi-implicit finite difference schemes as well as monotone dependence of the solution on the right-hand side are proved. Geometric rate of convergence for the iterative methods is investigated.
Splitting iterative methods for the sum of maximal monotone and single-valued monotone operators in a finite-dimensional space are studied. Convergence, rate of convergence and optimal iterative parameters are derived. A two-stage iterative method with inner iterations is analyzed in the case when both operators are linear, self-adjoint and positive definite.
Several new finite-difference schemes for a nonlinear convection-diffusion problem are constructed and numerically studied. These schemes are constructed on the basis of non-overlapping domain decomposition and predictor-corrector approach. Different non-overlapping decompositions of a domain, with cross-points and angles, schemes with grid refinement in time in some subdomains, are used. All proposed algorithms are extensively numerically tested and are founded stable and accurate under natural assumptions for time and space grid steps.
The advantages and disadvantages of the numerical methods are clearly seen in the numerical examples. All of the algorithms presented are quite easy and straight forward, from an implementation point of view. The speedups show that splitting iterative method can be parallelized better than multiplicative or additive Schwarz alternating method.
The numerical examples show that the multidecomposition method is a very effective numerical method for solving the continuous casting problem. The idea of dividing the subdomains to smaller subdomains seems to be very beneficial and profitable. The advantages of multidecomposition methods over other methods is obvious. Multidecomposition methods are extremely quick, while being just as accurate as other methods. The numerical results for one processor seem to be very promising
SERGEY YURIEVICH PREOBRAZHENSKY, SCHOLAR AND AUTHOR OF VERSES
No full textThe article is written in memoria of Sergey Yurievich Preobrahzhensky, linguist and poet. It tackles upon the scientific interests of the scholar, deals with his principal concepts in prosody and other spheres of poetics. Besides, It also contains a brief characteristics and examples of his own poetic work
Sergey Witte and his Foreign Investment Policy in the studies by English-speaking scholars
No full text. The article discusses the development of the interest of English-speaking historians in the foreign investment policy of Sergey Witte. The paper also examines the role of the Secret Memorandum of Sergey Wittein the understanding of the foreign investment in the Russian economy. The author shows that Russian and English-speaking historians, despite the political upheavals of the 20th century, were engaged in a scholarly conversation in their discussion of the subject
International Conference for Mathematical Modeling and Optimization in Mechanics, 6-7 March, 2014, Jyväskylä, Finland : honor of the 70th anniversary of Prof. Nikolay Banichuk
No full textThis book of abstracts presents materials of the International Conference for Mathematical Modeling
and Optimization in Mechanics (MMOM 2014) 6-7 March 2014, Jyväskylä, Finland. This event is
dedicated to Professor Nikolay Banichuk in occasion of his 70th anniversary.
It is aimed to present the latest results of leading scientists in mathematical modeling, numerical
analysis, and optimization theory and to discuss the state of the art and open problems in the field.
The book is divided in five sections:
1. Mathematical Modelling of Complex Systems
2. Stability Analysis and Vibration
3. Optimization
4. Methods of Numerical Analysis
5. Shape Optimizationunknown accessibilityei tietoa saavutettavuudest
An Overview of Economics
No full textI assume that your objective of ’Economics 101’ is to try to understand how the economy works instead of going through an economic curriculum. If so you are guaranteed to have fun. I personally undertook a similar journey ten years back. I would say that it is better to understand the principles of economics and then try to understand the economy/economic situation of any given country. My recommendations (for BSc students and everyone who is interested in economics101) are based on my own readings: Sloman’s ”Essentials of economics;” Gwartney et al. ”Economics: Private Public Choice;” Jesus Huerta de Soto’s ”The Austrian School: Market Order and Entrepreneurial Creativity;” Rodrik’s ”Economics Rules;” Foley’s ”Adam’s fallacy: a guide to economic theology;” De Soto’s ”The mystery of capital: Why capitalism triumphs in the West and fails everywhere else;” Harford’s ”The Undercover Economist;” Levitt and Dubner’s ”Freakonomics.”This Paper should not be reported as representing the views of Central Bank of Armenia. The views in this paper are those of the author and should not be interpreted as those of Central Bank of Armenia
An Overview of Economics
No full textI assume that your objective of ’Economics 101’ is to try to understand how the economy works instead of going through an economic curriculum. If so you are guaranteed to have fun. I personally undertook a similar journey ten years back. I would say that it is better to understand the principles of economics and then try to understand the economy/economic situation of any given country. My recommendations (for BSc students and everyone who is interested in economics101) are based on my own readings: Sloman’s ”Essentials of economics;” Gwartney et al. ”Economics: Private Public Choice;” Jesus Huerta de Soto’s ”The Austrian School: Market Order and Entrepreneurial Creativity;” Rodrik’s ”Economics Rules;” Foley’s ”Adam’s fallacy: a guide to economic theology;” De Soto’s ”The mystery of capital: Why capitalism triumphs in the West and fails everywhere else;” Harford’s ”The Undercover Economist;” Levitt and Dubner’s ”Freakonomics.”This Paper should not be reported as representing the views of Central Bank of Armenia. The views in this paper are those of the author and should not be interpreted as those of Central Bank of Armenia
Plato’s Gorgius: an attempt to an axiological commentary
No full textIn his new paper Sergey S. Avanesov (Tomsk State University) analyses the concepts of ‘intermediate’ being, ‘preference’ and the hierarchy of values developed in Plato’s dialogue against the background of Classical moral philosophy. This study of Ancient axiology continues a previous article by the same author, also published in this journal (vol. I, issue 2)
Modern creator in Sergey Samsonov\u27s novel The Kamlayev Anomaly
No full textВ статье рассматривается роман "Аномалия Камлаева" Сергея Самсонова. В центре внимания проблема творца и его творения. Автор максимально укрупняет понятие творчества, выводя его из сферы музыки в сферу самой жизни. Самсонов анализирует состояние человека 21 века и причины его духовного кризиса. Творчество Самсонова рассматривается в контексте нового реализма, сложившегося в русской литературе в конце 20 века. Творческий метод Самсонова также соотносится с дискуссионной концепцией метамодернизма.The article is devoted to the novel of Sergey Samsonov – The Kamlayev Anomaly. The focus is on the issue of a creative man and his creations. The author maximizes the notion of creative work, going beyond the limits of the sphere of music and bringing it to the sphere of life itself. Samsonov is trying to analyze the state of being of the 21st century human and the cause of human spiritual crisis. Samsonov\u27s writing is considered in the context of the new realism. Author\u27s creative method is also compared with the debatable concept of metamodermism
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