Additive Operator Difference Schemes

Author : Petr N. Vabishchevich
Publisher : Walter de Gruyter
Page : 370 pages
File Size : 42,6 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9783110321463

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Additive Operator-Difference Schemes by Petr N. Vabishchevich Pdf

Applied mathematical modeling is concerned with solving unsteady problems. Splitting schemes are attributed to the transition from a complex problem to a chain of simpler problems. This book shows how to construct additive difference schemes (splitting schemes) to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods) and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for systems of equations. The book is written for specialists in computational mathematics and mathematical modeling. All topics are presented in a clear and accessible manner.

Author : A.A. Samarskii,P.P. Matus,P.N. Vabishchevich
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 41,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401598743

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Difference Schemes with Operator Factors by A.A. Samarskii,P.P. Matus,P.N. Vabishchevich Pdf

Two-and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically non stationary problems of mathematical physics. In the theoretical analysis of difference schemes our basic attention is paid to the problem of sta bility of a difference solution (or well posedness of a difference scheme) with respect to small perturbations of the initial conditions and the right hand side. The theory of stability of difference schemes develops in various di rections. The most important results on this subject can be found in the book by A.A. Samarskii and A.V. Goolin [Samarskii and Goolin, 1973]. The survey papers of V. Thomee [Thomee, 1969, Thomee, 1990], A.V. Goolin and A.A. Samarskii [Goolin and Samarskii, 1976], E. Tad more [Tadmor, 1987] should also be mentioned here. The stability theory is a basis for the analysis of the convergence of an approximative solu tion to the exact solution, provided that the mesh width tends to zero. In this case the required estimate for the truncation error follows from consideration of the corresponding problem for it and from a priori es timates of stability with respect to the initial data and the right hand side. Putting it briefly, this means the known result that consistency and stability imply convergence.

Author : Oleg P. Iliev,Svetozar D. Margenov,Peter D Minev,Panayot S. Vassilevski,Ludmil T Zikatanov
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 51,8 Mb
Release : 2013-06-04
Category : Mathematics
ISBN : 9781461471721

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Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications by Oleg P. Iliev,Svetozar D. Margenov,Peter D Minev,Panayot S. Vassilevski,Ludmil T Zikatanov Pdf

One of the current main challenges in the area of scientific computing​ is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented. Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.

Author : Ivan Dimov,István Faragó,Lubin Vulkov
Publisher : Springer
Page : 583 pages
File Size : 50,7 Mb
Release : 2013-10-01
Category : Computers
ISBN : 9783642415159

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Numerical Analysis and Its Applications by Ivan Dimov,István Faragó,Lubin Vulkov Pdf

This book constitutes thoroughly revised selected papers of the 5th International Conference on Numerical Analysis and Its Applications, NAA 2012, held in Lozenetz, Bulgaria, in June 2012. The 65 revised papers presented were carefully reviewed and selected from various submissions. The papers cover a broad area of topics of interest such as numerical approximation and computational geometry; numerical linear algebra and numerical solution of transcendental equation; numerical methods for differential equations; numerical stochastics, numerical modeling; and high performance scientific computing.

Author : Sergey Lemeshevsky,Piotr Matus,Dmitriy Poliakov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 246 pages
File Size : 43,6 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9783110489729

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Exact Finite-Difference Schemes by Sergey Lemeshevsky,Piotr Matus,Dmitriy Poliakov Pdf

Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography

Author : Ivan Lirkov,Svetozar Margenov,Zahari Zlatev
Publisher : Springer Science & Business Media
Page : 570 pages
File Size : 53,9 Mb
Release : 2003
Category : Numerical analysis
ISBN : 9783540006084

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Numerical Methods and Applications by Ivan Lirkov,Svetozar Margenov,Zahari Zlatev Pdf

Author : Juergen Geiser
Publisher : Springer
Page : 325 pages
File Size : 55,9 Mb
Release : 2015-08-21
Category : Technology & Engineering
ISBN : 9783319151175

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Multicomponent and Multiscale Systems by Juergen Geiser Pdf

This book examines the latest research results from combined multi-component and multi-scale explorations. It provides theory, considers underlying numerical methods and presents brilliant computational experimentation. Engineering computations featured in this monograph further offer particular interest to many researchers, engineers and computational scientists working in frontier modeling and applications of multicomponent and multiscale problems. Professor Geiser gives specific attention to the aspects of decomposing and splitting delicate structures and controlling decomposition and the rationale behind many important applications of multi-component and multi-scale analysis. Multicomponent and Multiscale Systems: Theory, Methods and Applications in Engineering also considers the question of why iterative methods can be powerful and more appropriate for well-balanced multiscale and multicomponent coupled nonlinear problems. The book is ideal for engineers and scientists working in theoretical and applied areas.

Author : Alexander A. Samarskii
Publisher : CRC Press
Page : 796 pages
File Size : 48,9 Mb
Release : 2001-03-29
Category : Mathematics
ISBN : 0203908511

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The Theory of Difference Schemes by Alexander A. Samarskii Pdf

The Theory of Difference Schemes emphasizes solutions to boundary value problems through multiple difference schemes. It addresses the construction of approximate numerical methods and computer algorithms for solving mathematical physics problems. The book also develops mathematical models for obtaining desired solutions in minimal time using direct or iterative difference equations. Mathematical Reviews said it is "well-written [and] an excellent book, with a wealth of mathematical material and techniques."

Author : Aleksandr Andreevich Samarskiĭ,Petr Nikolaevich Vabishchevich
Publisher : Walter de Gruyter
Page : 456 pages
File Size : 55,7 Mb
Release : 2007
Category : Mathematics
ISBN : 3110196662

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Numerical Methods for Solving Inverse Problems of Mathematical Physics by Aleksandr Andreevich Samarskiĭ,Petr Nikolaevich Vabishchevich Pdf

"In direct problems for mathematical physics, the solution of partial differential equations supplemented with some boundary and initial conditions is to be determined. In many applications some of these conditions are missing, e.g., initial or boundary conditions, coefficients and right-hand sides of the equation may be unknown. Those problems are called inverse problems, and quite frequently, those problems turn out to be ill-posed, requiring some regularization methods for their approximate solution." "In the present monograph, the main classes of inverse problems in mathematical physics and their numerical treatment are considered. Many numerical illustrations and codes for their realization are included. The book is intended for graduate students and scientists interested in applied mathematics, computational mathematics and mathematical modeling."--BOOK JACKET.

Author : Ivan Lirkov,Svetozar Margenov
Publisher : Springer
Page : 610 pages
File Size : 49,6 Mb
Release : 2018-01-10
Category : Computers
ISBN : 9783319734415

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Large-Scale Scientific Computing by Ivan Lirkov,Svetozar Margenov Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the 11th International Conference on Large-Scale Scientific Computations, LSSC 2017, held in Sozopol, Bulgaria, in June 2017. The 63 revised short papers together with 3 full papers presented were carefully reviewed and selected from 63 submissions. The conference presents results from the following topics: Hierarchical, adaptive, domain decomposition and local refinement methods; Robust preconditioning algorithms; Monte Carlo methods and algorithms; Numerical linear algebra; Control and optimization; Parallel algorithms and performance analysis; Large-scale computations of environmental, biomedical and engineering problems. The chapter 'Parallel Aggregation Based on Compatible Weighted Matching for AMG' is available open access under a CC BY 4.0 license.

Author : Serge_ L_vovich Sobolev R. A. Aleksandrjan
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 46,5 Mb
Release : 1976-12-31
Category : Mathematics
ISBN : 0821895435

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Partial Differential Equations by Serge_ L_vovich Sobolev R. A. Aleksandrjan Pdf

Author : Anonim
Publisher : Unknown
Page : 506 pages
File Size : 43,8 Mb
Release : 2000
Category : Mathematics
ISBN : UOM:39015050421851

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Doklady by Anonim Pdf

Author : Aleksandr Andreevich Samarskiĭ
Publisher : Unknown
Page : 160 pages
File Size : 40,8 Mb
Release : 1998
Category : Finite differences
ISBN : UOM:39015051605239

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Second International Conference "Finite-Difference Methods, Theory and Application" (CFDM98) by Aleksandr Andreevich Samarskiĭ Pdf

Author : Ivan Dimov,Stefka Fidanova,Ivan Lirkov
Publisher : Springer
Page : 312 pages
File Size : 53,8 Mb
Release : 2015-02-03
Category : Computers
ISBN : 9783319155852

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Numerical Methods and Applications by Ivan Dimov,Stefka Fidanova,Ivan Lirkov Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on Numerical Methods and Applications, NMA 2014, held in Borovets, Bulgaria, in August 2014. The 34 revised full papers presented were carefully reviewed and selected from 56 submissions for inclusion in this book. The papers are organized in the following topical sections: Monte Carlo and quasi-Monte Carlo methods; metaheuristics for optimization problems; advanced numerical methods for scientific computing; advanced numerical techniques for PDEs and applications; solving large engineering and scientific problems with advanced mathematical models; numerical simulations and back analysis in civil and mechanical engineering.

Author : Anders Heyden,Gunnar Sparr,Mads Nielsen,Peter Johansen
Publisher : Springer
Page : 820 pages
File Size : 43,9 Mb
Release : 2003-08-01
Category : Computers
ISBN : 9783540479697

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Computer Vision - ECCV 2002 by Anders Heyden,Gunnar Sparr,Mads Nielsen,Peter Johansen Pdf

Premiering in 1990 in Antibes, France, the European Conference on Computer Vision, ECCV, has been held biennially at venues all around Europe. These conferences have been very successful, making ECCV a major event to the computer vision community. ECCV 2002 was the seventh in the series. The privilege of organizing it was shared by three universities: The IT University of Copenhagen, the University of Copenhagen, and Lund University, with the conference venue in Copenhagen. These universities lie ̈ geographically close in the vivid Oresund region, which lies partly in Denmark and partly in Sweden, with the newly built bridge (opened summer 2000) crossing the sound that formerly divided the countries. We are very happy to report that this year’s conference attracted more papers than ever before, with around 600 submissions. Still, together with the conference board, we decided to keep the tradition of holding ECCV as a single track conference. Each paper was anonymously refereed by three different reviewers. For the ?nal selection, for the ?rst time for ECCV, a system with area chairs was used. These met with the program chairsinLundfortwodaysinFebruary2002toselectwhatbecame45oralpresentations and 181 posters.Also at this meeting the selection was made without knowledge of the authors’identity.