UID:
almafu_9958099643602883
Umfang:
1 online resource (189 p.)
ISBN:
1-282-28990-X
,
9786612289903
,
0-08-095552-5
Serie:
Mathematics in science and engineering ; v. 44
Inhalt:
Nonlinear two point boundary value problems
Anmerkung:
Description based upon print version of record.
,
Front Cover; Nonlinear Two Point Boundary Value Problems; Copyright Page; Contents; Preface; Chapter 1. Introduction; 1. Kinds of Boundary Value Problems to Be Treated; 2. The Generalized Lipschitz Condition; 3. How Existence and Uniqueness Fail for Linear Boundary Value Problems; 4. A Simple Nonlinear Boundary Value Problem; 5. Standard Results concerning Initial Value Problems; Comments and Bibliography; Chapter 2. Relations between the First and Second Boundary Value Problems; 1. Relation between Uniqueness Intervals; 2. Relation between Existence Intervals; Chapter 3. Picard's Iteration
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1. Introduction2. Contraction Mappings; 3. Boundary Value Problems; 4. A More General Lipschitz Condition; 5. An Improved Error Bound for the Picard Iterates; 6. Extensions; Comments and Bibliography; Chapter 4. The Distance between Zeros and the Uniqueness Interval; 1. Introduction; 2. The Connection between Uniqueness and the Zeros of Unforced Equations; 3. Distance between Zeros for Unforced Equations; Comments and Bibliography; Chapter 5. Comparison Theorems; 1. Introduction; 2. Main Comparison Theorems; 3. Comparison Theorems for Weak Differential Inequalities; Comments and Bibliography
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Chapter 6. Principal Existence Theorems1. Introduction; 2. Solutions of the Comparison Problems; 3. Existence Theorems; Comments and Bibliography; Chapter 7. Further Existence and Uniqueness Results; 1. Introduction; 2. Existence in the Nonsingular Case; 3. Existence in the Singular Case; 4. A General Uniqueness Theorem; 5. Illustrative Examples; Comments and Bibliography; Chapter 8. Numerical Solution by Initial Value Methods; 1. Introduction; 2. A Convergence Criterion; 3. Lipschitzian Problems; Comments and Bibliography; Chapter 9. Numerical Solution by Boundary Value Methods
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1. Introduction2. A Modified Picard Iteration; 3. A Monotone Iteration; 4. Newton's Method; 5. Solution of Linear Problems by a Finite Difference Method; 6. Some Illustrative Examples; Comments and Bibliography; Index
,
English
Weitere Ausg.:
ISBN 0-12-073350-1
Sprache:
Englisch
Fachgebiete:
Mathematik
URL:
Volltext
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