Methods of nonlinear analysis. Volume 2 / Richard Bellman.

Format:

Book

Author/Creator:

Bellman, Richard, 1920-1984.

Series:

Mathematics in science and engineering ; v. 61, 2.

Mathematics in science and engineering ; v. 61, 2

Language:

English

Subjects (All):

Nonlinear theories.

Differential equations, Nonlinear.

Numerical analysis.

Physical Description:

1 online resource (281 p.)

Place of Publication:

New York ; London : Academic Press, 1973.

Language Note:

English

Summary:

Methods of nonlinear analysis

Contents:

Front Cover; Methods of Nonlinear Analysis; Copyright Page; Preface; Contents; Contents of Volume I; Chapter 9. Upper and Lower Bounds via Duality; 9.1. Introduction; 9.2. Guiding Idea; 9.3. A Simple Identity; 9.4. Quadratic Functional: Scalar Case; 9.5. min u J = max v H; 9.6. The Functional l t o [u'2 + g(u)] dt; 9.7. Geometric Aspects; 9.8. Multidimensional Case; 9.9. The Rayleigh-Ritz Method; 9.10. Alternative Approach; 9.11. J(u) = lto [u'2 + f(t)u2] dt; General f(t); 9.12. Geometric Aspects; Miscellaneous Exercises; Bibliography and Comments

Chapter 10. Caplygin's Method and Differential Inequalities10.1. Introduction; 10.2. The Caplygin Method; 10.3. The Equation u' < a(t)u + f (t); 10.4. The Linear Differential Inequality L(u) < f ( t ); 10.5. Elementary Approach; 10.6. An Integral Identity; 10.7. Strengthening of Previous Result; 10.8. Factorization of the Operator; 10.9. Alternate Proof of Monotonicity; 10.10. A Further Condition; 10.11. Two-point Boundary Conditions; 10.12. Variational Approach; 10.13. A Related Parabolic Partial Differential Equation; 10.14. Nonnegativity of u(t, s); 10.15. Limiting Behavior

10.16. Limiting Behavior: Energy Inequalities10.17. Monotonicity of Maximum; 10.18. Lyapunov Functions; 10.19. Factorization of the nth-order Linear Operator; 10.20. A Result for the nth-order Linear Differential Equation; 10.21. An Example; 10.22. Linear Systems; 10.23. Partial Differential Equation-I; 10.24. Partial Differential Equation-II; Miscellaneous Exercises; Bibliography and Comments; Chapter 11. Quasilinearization; 11.1. Introduction; 11.2. The Riccati Equation; 11.3. Explicit Representation; 11.4. Successive Approximations and Monotone Convergence

11.5. Maximum Interval of Convergence11.6. Dini's Theorem and Uniform Convergence; 1 1.7. Newton-Raphson-Kantorovich Approximation; 11.8. Quadratic Convergence; 11.9. Upper Bounds; 11.10. u' = g(u, t ); 11.11. Random Equation; 11.12. Upper and Lower Bounds; 1 I. 13. Asymptotic Behavior; 11.14. Multidimensional Riccati Equation; 11.15. Two-point Boundary Value Problems; 11.16. Maximum Interval of Convergence; 11.1 7. Quadratic Convergence; 11.18. Discussion; 11.19. Computational Feasibility; 11.20. Elliptic Equations; 11.21. Parabolic Equations; 1 1.22. Minimum and Maximum Principles

Miscellaneous ExercisesBibliography and Comments; Chapter 12. Dynamic Programming; 12.1. Introduction; 12.2. Multistage Processes; 12.3. Continuous Version; 12.4. Multistage Decision Processes; 12.5. Stochastic and Adaptive Processes; 12.6. Functional Equations; 12.7. Infinite Stage Process; 12.8. Policy; 12.9. Approximation in Policy Space; 12.10. Discussion; 12.11. Calculus of Variations as a Multistage Decision Process; 12.12. A New Formalism; 12.13. The Principle of Optimality; 12.14. Quadratic Case; 12.15. Multidimensional Case; 12.1 6. Computational Feasibility; 12.17. Stability

12.18. Computational Feasibility: General Case-I

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-282-28982-9

9786612289828

0-08-095571-1

OCLC:

428099569