| Description |
1 online resource (xvii, 238 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Mathematics and statistics |
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Mathematics and statistics series (ISTE)
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| Bibliography |
Includes bibliographical references (pages 223-236) and index. |
| Note |
Print version record. |
| Contents |
Front Cover ; Dedication ; Factorization of Boundary Value Problems Using the Invariant Embedding Method; Copyright ; Contents; Preface; Chapter 1. Presentation of the Formal Computation of Factorization; 1.1. Definition of the model problem and its functional framework; 1.2. Direct invariant embedding; 1.3. Backward invariant embedding; 1.4. Internal invariant embedding; Chapter 2. Justification of the Factorization Computation; 2.1. Functional framework; 2.2. Semi-discretization; 2.3. Passing to the limit; Chapter 3. Complements to the Model Problem. |
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3.1. An alternative method for obtaining the factorization3.2. Other boundary conditions; 3.3. Explicitly taking into account the boundary conditions and the right-hand side; 3.4. Periodic boundary conditions in x; 3.5. An alternative but unstable formulation; 3.6. Link with the Steklov-Poincaré operator; 3.7. Application of the Schwarz kernel theorem: link with Green's functions and Hadamard's formula; Chapter 4. Interpretation of the Factorization through a Control Problem; 4.1. Formulation of problem (P0) in terms of optimal control. |
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4.2. Summary of results on the decoupling of optimal control problems4.3. Summary of results of A. Bensoussan on Kalman optimal filtering; 4.4. Parabolic regularization for the factorization of elliptic boundary value problems; Chapter 5. Factorization of the Discretized Problem; 5.1. Introduction and problem statement; 5.2. Application of the factorization method to problem (Ph); 5.3. A second method of discretization; 5.4. A third possibility: centered scheme; 5.5. Row permutation; 5.6. Case of a discretization of the section by finite elements; Chapter 6. Other Problems. |
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6.1. General second-order linear elliptic problems6.2. Systems of coupled boundary value problems; 6.3. Linear elasticity system; 6.4. Problems of order higher than 2; 6.5. Stokes problems; 6.6. Parabolic problems; Chapter 7. Other Shapes of Domain; 7.1. Domain generalization: transformation preserving orthogonal coordinates; 7.2. Quasi-cylindrical domains with normal velocity fields; 7.3. Sweeping the domain by surfaces of arbitrary shape; Chapter 8. Factorization by the QR Method; 8.1. Normal equation for problem (P0) in section 1.1. |
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8.2. Factorization of the normal equation by invariant embedding8.3. The QR method; Chapter 9. Representation Formulas for Solutions of Riccati Equations; 9.1. Representation formulas; 9.2. Diagonalization of the two-point boundary value problem; 9.3. Homographic representation of P(x); 9.4. Factorization of problem (P0) with a Dirichlet condition at x =0; Appendix. Gaussian LU Factorization as a Method of Invariant Embedding; A.1. Invariant embedding for a linear system; A.2. Block tridiagonal systems; Bibliography; Index; Back Cover. |
| Subject |
Boundary value problems.
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Factorization (Mathematics)
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Invariant imbedding.
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Problèmes aux limites.
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Factorisation.
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Plongement invariant.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Boundary value problems
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Factorization (Mathematics)
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Invariant imbedding
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| Added Author |
Ramos, Angel M., author.
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| Other Form: |
Print version: Henry, J. (Jacques). Factorization of boundary value problems using the invariant embedding method. London : ISTE Press Ltd ; Kidlington, Oxford : Elsevier Ltd, [2016] 1785481436 (OCoLC)945105395 |
| ISBN |
9780081010907 (electronic bk.) |
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0081010907 (electronic bk.) |
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1785481436 |
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9781785481437 |
| Standard No. |
AU@ 000059643857 |
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AU@ 000066135468 |
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AU@ 000068127234 |
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CHNEW 001013939 |
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DEBSZ 482475188 |
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GBVCP 879419881 |
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UKMGB 018075588 |
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