UID:
almafu_9958084935302883
Format:
1 online resource (237 p.)
ISBN:
1-282-75537-4
,
9786612755378
,
0-08-095609-2
Series Statement:
Mathematics in science and engineering ; v. 100
Content:
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-rank
Note:
Description based upon print version of record.
,
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
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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
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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
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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
,
English
Additional Edition:
ISBN 0-12-492950-8
Language:
English
