Computational methods in engineering boundary value problems, Volume 145 (Mathematics in Science and Engineering)

✍ Scribed by Na (editor)

• Publisher: Academic Press
• Year: 1980
• Tongue: English
• Leaves: 321
• Category: Library

✦ Table of Contents

Front Cover
Computational Methods in Engineering Boundary Value Problems
Copyright Page
Contents
Preface
Chapter 1. Introduction
1.1 Introduction
1.2 Methods of Solution
1.3 Numerical Integration of Initial Value Problems
1.4 Concluding Remarks
References
Chapter 2. Method of Superposition
2.1 Introduction
2.2 Reduction of Linear Boundary Value Problems to Initial Value Problems
2.3 Reduction of Third-Order Boundary Value Problems to Initial Value Problems
2.4 Concluding Remarks
Problems
References
Chapter 3. Method of Chasing
3.1 Introduction
3.2 Derivation of Equations of Chasing By Jones—Second-Order Differential Equations
3.3 Application of the Method
3.4 Third-Order Differential Equations
3.5 Concluding Remarks
Problems
References
Chapter 4. The Adjoint Operator Method
4.1 Introduction
4.2 Second-Order Differential Equations
4.3 Third-Order Differential Equations
4.4 Concluding Remarks
Problems
References
Chapter 5. Iterative Methods—The Shooting Methods
5.1 Introduction
5.2 Newton's Method
5.3 Parallel Shooting
5.4 Quasi Linearization
5.5 Concluding Remarks
Problems
References
Chapter 6. Iterative Methods—The Finite-Difference Method
6.1 Introduction
6.2 Finite Differences
6.3 Solution of Boundary Value Problems by Finite Difference
6.4 Second-Order Differential Equations
6.5 Third-Order Differential Equations
6.6 First-Order System and Newton's Method
6.7 Concluding Remarks
Problems
References
Chapter 7. Method of Transformation—Direct Transformation
7.1 Introduction
7.2 Transformation for a Given Group of Transformations
7.3 Extension of the Transformation Method for a Given Group of Transformations
7.4 Uniqueness of the Solution
Problems
References
Chapter 8. Method of Transformation—Reduced Physical Parameters
8.1 Introduction
8.2 Reduced Physical Parameters
8.3 Application to Simultaneous Differential Equations
8.4 Application to an Eigenvalue Problem
8.5 Concluding Remarks
Problems
References
Chapter 9. Method of Transformation—Invariance of Physical Parameters
9.1 Introduction
9.2 Boundary Value Problem with Two or More Parameters
9.3 Systematic Search of Multiple Solutions
9.4 Thin Struts with Large Elastic Displacement
Problems
References
Chapter 10. Method of Parameter Differentiation
10.1 Introduction
10.2 Nonlinear Algebraic Equations
10.3 Parameter Differentiation Applied to Differential Equations
10.4 Application to Simultaneous Equations
10.5 The General Parameter Mapping (GPM) of Kubicek and Hlavecek
10.6 Method of Continuation of Roberts and Shipman
10.7 Concluding Remarks
Problems
References
Chapter 11. Method of Invariant Imbedding
11.1 Introduction
11.2 Concept of Invariant Imbedding
11.3 Isothermal Packed-Bed Chemical Reactor
11.4 Radiation Fins
11.5 Solution of Falkner–Skan Equation
11.6 Concluding Remarks
Problems
References
Chapter 12. Integral Equation Method
12.1 Introduction
12.2 Linear Boundary Value Problems
12.3 Nonlinear Boundary Value Problems
12.4 Concluding Remarks
Problems
References
Index