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Initial value methods for boundary value problems : theory and application of invariant imbedding / [edited by] Gunter H. Meyer
Mitwirkende(r): Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Mathematics in science and engineering ; v. 100Verlag: New York : Academic Press, 2010Beschreibung: Online Ressource (xiii, 220 pages) : illustrationsISBN:- 9780124929500
- 9780080956091
- 0080956092
- 0124929508
- 9780124929500
- Gewöhnliche Differentialgleichung
- Randwertproblem
- Invariante Einbettung
- Partielle Differentialgleichung
- Boundary value problems
- Initial value problems
- Problèmes aux limites
- Problèmes aux valeurs initiales
- Plongement invariant
- Invariant imbedding
- problème valeur propre
- problème interface
- équation Riccati
- problème aux limites
- Anfangswertproblem
- MATHEMATICS ; Differential Equations ; General
- Matematica Da Computacao
- Electronic books
- 515.35
- QA379
Inhalte:
Zusammenfassung: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rankPPN: PPN: 878888225Package identifier: Produktsigel: BSZ-33-EBS-C1UB | BSZ-33-EBS-HSAA | GBV-33-EBS-MRI | GBV-33-EBS-ZHB | GBV-33-Freedom-BL | ZDB-1-ELC | ZDB-33-EBS | ZDB-33-ESD
Front Cover; Initial Value Methods for Boundary Value Problems: Theory and Application of Invariant Imbedding; Copyright Page; Contents; Preface; Acknowledgments; Introduction; 0.1. An Outline of the Monograph; 0.2. Notation; 0.3. Background Material; Chapter 1. Characteristic Theory; 1.1. First-Order Partial Differential Equations with the Same Principal Part; 1.2. Linear Characteristic Equations; 1.3. The Riccati Equation; 1.4. Nonlinear Characteristic Equations; 1.5. Discrete Evolution Equations; Notes; Chapter 2. Two-Point Boundary value Problems
2.1. Initial Value Techniques for Boundary Value Problems-A Survey2.2. Derivation of the Invariant Imbedding Equation; 2.3. Existence Theorems for Two-Point Boundary Value Problems; 2.4. The Numerical Solution of Nonlinear Two-Point Boundary Value Problems; 2.5. Numerical Examples; 2.6. Linear Problems; 2.7. Numerical Considerations for Linear Problems; 2.8. Solving Potential and Diffusion Problems; 2.9. Nonlinear Boundary Conditions; 2.10. Free Boundary Problems; 2.11. Discrete Two-Point Boundary Value Problems; Notes; Chapter 3. Interface Problems
3.1. The Invariant Imbedding Equations for Interface Problems3.2. Linear Interface Problems; 3.3. Free Interface Problems; 3.4. Dynamic Programming; 3.5. Overcoming Critical Lengths; Notes; Chapter 4. Multipoint Boundary Value Problems; 4.1. The Invariant Imbedding Equations; 4.2. Linear Multipoint Problems; Notes; Chapter 5. Invariant Imbedding for Abstract Equations; 5.1. Differential Equations in a Banach Space; 5.2. Invariant Imbedding for Linear Evolution Equations; 5.3. Invariant Imbedding for Mild Solutions; Notes; Chapter 6. Infinite-Dimensional Riccati Equations
6.1. Local Existence Theorems6.2. Non-Hermitian Equations with Bounded Coefficients; 6.3. Non-Hermitian Equations With Unbounded Coefficients; 6.4. Hermitian Equations; References; Index
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