Numerical methods grid equations von samarskij a a (31 Ergebnisse)

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 5 The Mathematical Theory of Iterative Methods.- 5.1 Several results from functional analysis.- 5.2 Difference schemes as operator equations.- 5.3 Basic concepts from the theory of iterative methods.- 6 Two-Level Iterative Methods.- 6.1 Choosing the iterative parameters.- 6.2 The Chebyshev two-level method.- 6.3 The simple iteration method.- 6.4 The non-self-adjoint case. The simple iteration method.- 6.5 Sample applications of the iterative methods.- 7 Three-Level Iterative Methods.- 7.1 An estimate of the convergence rate.- 7.2 The Chebyshev semi-iterative method.- 7.3 The stationary three-level method.- 7.4 The stability of two-level and three-level methods relative to a priori data.- 8 Iterative Methods of Variational Type.- 8.1 Two-level gradient methods.- 8.2 Examples of two-level gradient methods.- 8.3 Three-level conjugate-direction methods.- 8.4 Examples of the three-level methods.- 8.5 Accelerating the convergence of two-level methods in the self-adjoint case.- 9 Triangular Iterative Methods.- 9.1 The Gauss-Seidel method.- 9.2 The successive over-relaxation method.- 9.3 Triangular methods.- 10 The Alternate-Triangular Method.- 10.1 The general theory of the method.- 10.2 Boundary-value difference problems for elliptic equations in a rectangle.- 10.3 The alternate-triangular method for elliptic equations in arbitrary regions.- 11 The Alternating-Directions Method.- 11.1 The alternating-directions method in the commutative case.- 11.2 Sample applications of the method.- 11.3 The alternating-directions method in the general case.- 12 Methods for Solving Equationswith Indefinite and Singular Operators.- 12.1 Equations with real indefinite operators.- 12.2 Equations with complex operators.- 12.3 General iterative methods for equations with singular operators.- 12.4Special methods.- 13 Iterative Methods for Solving Non-Linear Equations.- 13.1 Iterative methods. The general theory.- 13.2 Methods for solving non-linear difference schemes.- 14 Example Solutions of Elliptic Grid Equations.- 14.1 Methods for constructing implicit iterative schemes.- 14.3 Systems of elliptic equations.- 14.4 Methods for solving elliptic equations in irregular regions.- 15 Methods for Solving Elliptic Equationsin Curvilinear Orthogonal Coordinates.- 15.1 Posing boundary-value problems for differential equations.- 15.2 The solution of difference problems in cylindrical coordinates.- 15.3 Solution of difference problems in polar coordinate systems.- Appendices.- Construction of the minimax polynomial.- Translator's note.…

Taschenbuch. Zustand: Neu. Numerical Methods for Grid Equations | Volume II Iterative Methods | A. A. Samarskij (u. a.) | Taschenbuch | xvi | Englisch | 2011 | Birkhäuser | EAN 9783034899239 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.…

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - The finite-difference solution of mathematical-physics differential equations is carried out in two stages: 1) the writing of the difference scheme (a differ ence approximation to the differential equation on a grid), 2) the computer solution of the difference equations, which are written in the form of a high order system of linear algebraic equations of special form (ill-conditioned, band-structured). Application of general linear algebra methods is not always appropriate for such systems because of the need to store a large volume of information, as well as because of the large amount of work required by these methods. For the solution of difference equations, special methods have been developed which, in one way or another, take into account special features of the problem, and which allow the solution to be found using less work than via the general methods. This work is an extension of the book Difference M ethod3 for the Solution of Elliptic Equation3 by A. A. Samarskii and V. B. Andreev which considered a whole set of questions connected with difference approximations, the con struction of difference operators, and estimation of the ~onvergence rate of difference schemes for typical elliptic boundary-value problems. Here we consider only solution methods for difference equations. The book in fact consists of two volumes. …

Taschenbuch. Zustand: Neu. Numerical Methods for Grid Equations | Volume I Direct Methods | A. A. Samarskij (u. a.) | Taschenbuch | xxxv | Englisch | 2011 | Birkhäuser | EAN 9783034899727 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.…

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Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 5 The Mathematical Theory of Iterative Methods.- 5.1 Several results from functional analysis.- 5.1.1 Linear spaces.- 5.1.2 Operators in linear normed spaces.- 5.1.3 Operators in a Hilbert space.- 5.1.4 Functions of a bounded operator.- 5.1.5 Operators in a.…

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Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -5 The Mathematical Theory of Iterative Methods.- 5.1 Several results from functional analysis.- 5.2 Difference schemes as operator equations.- 5.3 Basic concepts from the theory of iterative methods.- 6 Two-Level Iterative Methods.- 6.1 Choosing the iterative parameters.- 6.2 The Chebyshev two-level method.- 6.3 The simple iteration method.- 6.4 The non-self-adjoint case. The simple iteration method.- 6.5 Sample applications of the iterative methods.- 7 Three-Level Iterative Methods.- 7.1 An estimate of the convergence rate.- 7.2 The Chebyshev semi-iterative method.- 7.3 The stationary three-level method.- 7.4 The stability of two-level and three-level methods relative to a priori data.- 8 Iterative Methods of Variational Type.- 8.1 Two-level gradient methods.- 8.2 Examples of two-level gradient methods.- 8.3 Three-level conjugate-direction methods.- 8.4 Examples of the three-level methods.- 8.5 Accelerating the convergence of two-level methods in the self-adjoint case.- 9 Triangular Iterative Methods.- 9.1 The Gauss-Seidel method.- 9.2 The successive over-relaxation method.- 9.3 Triangular methods.- 10 The Alternate-Triangular Method.- 10.1 The general theory of the method.- 10.2 Boundary-value difference problems for elliptic equations in a rectangle.- 10.3 The alternate-triangular method for elliptic equations in arbitrary regions.- 11 The Alternating-Directions Method.- 11.1 The alternating-directions method in the commutative case.- 11.2 Sample applications of the method.- 11.3 The alternating-directions method in the general case.- 12 Methods for Solving Equationswith Indefinite and Singular Operators.- 12.1 Equations with real indefinite operators.- 12.2 Equations with complex operators.- 12.3 General iterative methods for equations with singular operators.- 12.4Special methods.- 13 Iterative Methods for Solving Non-Linear Equations.- 13.1 Iterative methods. The general theory.- 13.2 Methods for solving non-linear difference schemes.- 14 Example Solutions of Elliptic Grid Equations.- 14.1 Methods for constructing implicit iterative schemes.- 14.3 Systems of elliptic equations.- 14.4 Methods for solving elliptic equations in irregular regions.- 15 Methods for Solving Elliptic Equationsin Curvilinear Orthogonal Coordinates.- 15.1 Posing boundary-value problems for differential equations.- 15.2 The solution of difference problems in cylindrical coordinates.- 15.3 Solution of difference problems in polar coordinate systems.- Appendices.- Construction of the minimax polynomial.- Translator's note.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 524 pp. Englisch.…

Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -The finite-difference solution of mathematical-physics differential equations is carried out in two stages: 1) the writing of the difference scheme (a differ ence approximation to the differential equation on a grid), 2) the computer solution of the difference equations, which are written in the form of a high order system of linear algebraic equations of special form (ill-conditioned, band-structured). Application of general linear algebra methods is not always appropriate for such systems because of the need to store a large volume of information, as well as because of the large amount of work required by these methods. For the solution of difference equations, special methods have been developed which, in one way or another, take into account special features of the problem, and which allow the solution to be found using less work than via the general methods. This work is an extension of the book Difference M ethod3 for the Solution of Elliptic Equation3 by A. A. Samarskii and V. B. Andreev which considered a whole set of questions connected with difference approximations, the con struction of difference operators, and estimation of the ~onvergence rate of difference schemes for typical elliptic boundary-value problems. Here we consider only solution methods for difference equations. The book in fact consists of two volumes.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 284 pp. Englisch.…

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