The Theory Of Difference Schemes
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The Theory Of Difference Schemes
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Author : Alexander A. Samarskii
language : en
Publisher: CRC Press
Release Date : 2001-03-29
The Theory Of Difference Schemes written by Alexander A. Samarskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-29 with Mathematics categories.
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."
Difference Schemes
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Author : S.K. Godunov
language : en
Publisher: Elsevier
Release Date : 1987-05-01
Difference Schemes written by S.K. Godunov and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-05-01 with Mathematics categories.
Much applied and theoretical research in natural sciences leads to boundary-value problems stated in terms of differential equations. When solving these problems with computers, the differential problems are replaced approximately by difference schemes.This book is an introduction to the theory of difference schemes, and was written as a textbook for university mathematics and physics departments and for technical universities. Some sections of the book will be of interest to computations specialists.While stressing a mathematically rigorous treatment of model problems, the book also demonstrates the relation between theory and computer experiments, using difference schemes created for practical computations.
Difference Schemes
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Author : Sergeĭ Konstantinovich Godunov
language : en
Publisher: Elsevier Science Limited
Release Date : 1987-01-01
Difference Schemes written by Sergeĭ Konstantinovich Godunov and has been published by Elsevier Science Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-01-01 with Mathematics categories.
Much applied and theoretical research in natural sciences leads to boundary-value problems stated in terms of differential equations. When solving these problems with computers, the differential problems are replaced approximately by difference schemes. This book is an introduction to the theory of difference schemes, and was written as a textbook for university mathematics and physics departments and for technical universities. Some sections of the book will be of interest to computations specialists. While stressing a mathematically rigorous treatment of model problems, the book also demonstrates the relation between theory and computer experiments, using difference schemes created for practical computations.
Difference Schemes With Operator Factors
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Author : A.A. Samarskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Difference Schemes With Operator Factors written by A.A. Samarskii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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.
New Difference Schemes For Partial Differential Equations
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Author : Allaberen Ashyralyev
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
New Difference Schemes For Partial Differential Equations written by Allaberen Ashyralyev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present monograph is devoted to the construction and investigation of the new high order of accuracy difference schemes of approximating the solutions of regular and singular perturbation boundary value problems for partial differential equations. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points. This approach permitted essentially to extend to a class of problems where the theory of difference methods is applicable. Namely, now it is possible to investigate the differential equations with variable coefficients and regular and singular perturbation boundary value problems. The investigation is based on new coercivity inequalities. The book will be of value to professional mathematicians, as well as advanced students in the fields of numerical analysis, functional analysis, and ordinary and partial differential equations.
Theory Of Difference Schemes
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Author : S. K. Godunov
language : nl
Publisher:
Release Date : 1964
Theory Of Difference Schemes written by S. K. Godunov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with categories.
Computer Aided Analysis Of Difference Schemes For Partial Differential Equations
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Author : Victor G. Ganzha
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-01
Computer Aided Analysis Of Difference Schemes For Partial Differential Equations written by Victor G. Ganzha and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-01 with Science categories.
Advances in computer technology have conveniently coincided withtrends in numerical analysis toward increased complexity ofcomputational algorithms based on finite difference methods. It isno longer feasible to perform stability investigation of thesemethods manually--and no longer necessary. As this book shows,modern computer algebra tools can be combined with methods fromnumerical analysis to generate programs that will do the jobautomatically. Comprehensive, timely, and accessible--this is the definitivereference on the application of computerized symbolic manipulationsfor analyzing the stability of a wide range of difference schemes.In particular, it deals with those schemes that are used to solvecomplex physical problems in areas such as gas dynamics, heat andmass transfer, catastrophe theory, elasticity, shallow watertheory, and more. Introducing many new applications, methods, and concepts,Computer-Aided Analysis of Difference Schemes for PartialDifferential Equations * Shows how computational algebra expedites the task of stabilityanalysis--whatever the approach to stability investigation * Covers ten different approaches for each stability method * Deals with the specific characteristics of each method and itsapplication to problems commonly encountered by numerical modelers * Describes all basic mathematical formulas that are necessary toimplement each algorithm * Provides each formula in several global algebraic symboliclanguages, such as MAPLE, MATHEMATICA, and REDUCE * Includes numerous illustrations and thought-provoking examplesthroughout the text For mathematicians, physicists, and engineers, as well as forpostgraduate students, and for anyone involved with numericsolutions for real-world physical problems, this book provides avaluable resource, a helpful guide, and a head start ondevelopments for the twenty-first century.
Additive Operator Difference Schemes
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Author : Petr N. Vabishchevich
language : en
Publisher: Walter de Gruyter
Release Date : 2013-11-27
Additive Operator Difference Schemes written by Petr N. Vabishchevich and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
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.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-08-31
Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-31 with Mathematics categories.
V.1. A-B v.2. C v.3. D-Feynman Measure. v.4. Fibonaccimethod H v.5. Lituus v.6. Lobachevskii Criterion (for Convergence)-Optical Sigman-Algebra. v.7. Orbi t-Rayleigh Equation. v.8. Reaction-Diffusion Equation-Stirling Interpolation Fo rmula. v.9. Stochastic Approximation-Zygmund Class of Functions. v.10. Subject Index-Author Index.
Encyclopaedia Of Mathematics Set
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-02-28
Encyclopaedia Of Mathematics Set written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-28 with Mathematics categories.
The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.