Dynamic programming and partial differential equations / Edward Angel, Richard Bellman.

Format:

Book

Author/Creator:

Angel, Edward.

Contributor:

Bellman, Richard, 1920-1984.

Series:

Mathematics in science and engineering ; v.88.

Mathematics in science and engineering ; v.88

Language:

English

Subjects (All):

Differential equations, Partial--Numerical solutions.

Differential equations, Partial.

Dynamic programming.

Invariant imbedding.

Differential equations, Partial--Data processing.

Physical Description:

1 online resource (219 p.)

Place of Publication:

New York : Academic Press, 1972.

Language Note:

English

Summary:

Dynamic programming and partial differential equations

Contents:

Front Cover; Dynamic Programming and Partial Differential Equations; Copyright Page; Contents; Preface; CHAPTER 1. INTRODUCTION; CHAPTER 2. QUADRATIC VARIATIONAL PROBLEMS; 1. Introduction; 2. Variational Approach; 3. Positive Definiteness, Existence, and Uniqueness of Solution; 4. Computational Aspects; 5. Vector-Matrix Case; 6. Rayleigh-Ritz Method; 7. Bubnov-Galerkin Method; Bibliography and Comment; CHAPTER 3. DYNAMIC PROGRAMMING; 1. Introduction; 2. Difference Equations; 3. Functional Equation; 4. Principle of Optimality; 5. Nonstationary Case; 6. Quadratic Functions

7. Minimum Convolution8. Acceleration of Calculation; 9. Differential Equations; 10. Quadratic Case; 11. Minimum Convolutions; 12. Tridiagonal Matrices; Bibliography and Comment; CHAPTER 4. THE POTENTIAL EQUATION; 1. Introduction; 2. The Euler-Langrange Equation; 3. Inhomogeneous and Nonlinear Cases; 4. Green's Function; 5. One-Dimensional Case; 6. Two-Dimensional Case; 7. Discretization; 8. Rectangular Region; 9. Rigorous Aspects; 10. Associated Minimization Problem; 11. Approximation from Above; 12. Discussion; 13. Semidiscretization; 14. Irregular Grid

15. Solution of the Difference Equations16. Iterative Solutions; 17. Limitations of the Iterative Approach; Miscellaneous Exercises; Bibliography and Comment; CHAPTER 5. DYNAMIC PROGRAMMING AND ELLIPTIC EQUATIONS; 1. The Potential Equation; 2. Discretization; 3. Matrix-Vector Formulation; 4. Dynamic Programming; 5. Recurrence Equations; 6. The Calculations; 7. Nonsingularity; 8. Stability; 9. Discussion; 10. Efficiency; 11. Example; 12. Deferred Passage to the Limit; 13. General Linear Equations; 14. Irregular Regions; 15. Higher Order Equations; 16. Distributed Control

Bibliography and CommentCHAPTER 6. INVARIANT IMBEDDING; 1. Invariant Imbedding; 2. The Riccati Transformation; 3. Single Sweep Methods; 4. Discretization; 5. Recurrence Relations; 6. Relation to Dynamic Programming; 7. Nonsingularity and Stability; 8. Relation to Gaussian Elimination; 9. Relation to the Riccati Equation; 10. Invariant Imbedding; 11. Continuous Invariant Imbedding; 12. Generalized Riccati Transformations; 13. The Biharmonic Equation; 14. Random Walk; 15. Invariant Imbedding and Random Walk; 16. Another Imbedding; Bibliography and Comment; CHAPTER 7. IRREGULAR REGIONS

1. Introduction2. Irregular Regions; 3. Case I: Order uR > Order uR-1; 4. Example; 5. Case II: Order uR < Order UR-1; 6. Example; 7. Nonsingularity and Stability; 8. Removal of Restrictions; 9. Examples; 10. General Linear Equations; 11. Other Boundary Conditions; 12. Three Dimensional Equations; 13. The Biharmonic Equation; 14. Invariant Imbedding and Difference Equations; 15. A Second Approach; 16. Matrix-Vector Equations; 17. General Regions; Bibliography and Comment; CHAPTER 8. SPECIAL COMPUTATIONAL METHODS; 1. Direct versus Iterative Methods; 2. The Characteristic Values of Q

3. Kronccker Product

Notes:

Description based upon print version of record.

Includes bibliographies.

ISBN:

1-282-28922-5

9786612289224

0-08-095597-5

OCLC:

316568122