Discrete Numerical Methods in Physics and Engineering
Published on 14. May 2014
325 pages
978-0-08-095616-9 (ISBN)
Description
Discrete Numerical Methods in Physics and Engineering
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Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095616-9 (9780080956169)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
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Donald Greenspan
Discrete Numerical Methods in Physics and Engineering
Book
01/1974
Academic Press
€71.19
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Content
- Front Cover
- Discrete Numerical Methods in Physics and Engineering
- Copyright Page
- Contents
- Preface
- Acknowledgments
- CHAPTER I. NUMERICAL SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL SYSTEMS
- 1.1 Introduction
- 1.2 Matrices and Linear Systems
- 1.3 Gauss Elimination
- 1.4 Tridiagonal Systems
- 1.5 The Generalized Newton's Method
- 1.6 Remarks
- Exercises
- CHAPTER II. APPROXIMATE SOLUTION OF PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
- 2.1 Introduction
- 2.2 Grid Points and Differences
- 2.3 The Method of Taylor Series
- 2.4 Runge-Kutta Methods
- 2.5 The Nonlinear Pendulum
- 2.6 Instability
- 2.7 Periodic Solutions of van der Pol's Equation
- 2.8 Approximate Solution of Boundary Value Problems
- 2.9 Remarks
- Exercises
- CHAPTER III. NUMERICAL SOLUTION OF ELLIPTIC BOUNDARY VALUE PROBLEMS
- 3.1 Introduction
- 3.2 Boundary Value Problems for the Laplace Equation
- 3.3 Difference Equation Approximation of Laplace's Equation
- 3.4 Interior and Boundary Lattice Points
- 3.5 The Numerical Method
- 3.6 Numerical Solution of the Exterior Dirichlet Problem
- 3.7 Remark on Neumann and Mixed Type Problems
- 3.8 The General Linear Elliptic Equation with Constant Coefficients
- 3.9 Extension to Three Dimensions
- 3.10 The Classical Problem of Capacity
- 3.11 Mildly Nonlinear Problems
- Exercises
- CHAPTER IV. NUMERICAL SOLUTION OF PARABOLIC DIFFERENTIAL EQUATIONS
- 4.1 Introduction
- 4.2 Stability
- 4.3 An Explicit Numerical Method
- 4.4 An Implicit Numerical Method
- 4.5 The Crank-Nicolson Method
- 4.6 Mildly Nonlinear Problems
- 4.7 A Boundary Value Technique
- Exercises
- CHAPTER V. NUMERICAL SOLUTION OF THE WAVE EQUATION
- 5.1 Introduction
- 5.2 The Cauchy Problem
- 5.3 Stability
- 5.4 An Explicit Method for Initial-Boundary Problems
- 5.5 An Implicit Method for Initial-Boundary Problems
- 5.6 A Second Implicit Method for Initial-Boundary Problems
- 5.7 Mildly Nonlinear Problems
- 5.8 A Boundary Value Technique
- 5.9 Other Methods
- Exercises
- CHAPTER VI. APPROXIMATE EXTREMIZATION OF FUNCTIONALS
- 6.1 Introduction
- 6.2 Extremization of Functionals
- 6.3 A Numerical Method
- 6.4 Geodesics
- 6.5 Free Boundary Value Problems
- 6.6 Variational Problems and Partial Differential Equations
- 6.7 The Plateau Problem
- Exercises
- CHAPTER VII. APPROXIMATE SOLUTION OF FLUID PROBLEMS
- 7.1 Introduction
- 7.2 A Prototype Liquid Problem
- 7.3 Biharmonic Problems
- 7.4 A Prototype Time Dependent Fluid Problem
- 7.5 A Boundary Value Technique
- 7.6 The Method of Fromm
- 7.7 The Method of Pearson
- 7.8 Remarks on Three Dimensional Problems
- 7.9 Hyperbolic Systems
- 7.10 Initial Value Problems
- 7.11 The Method of Courant, Isaacson. and Rees
- 7.12 The Lax-Wendroff Method
- 7.13 Other Methods
- Exercises
- CHAPTER VIII. DISCRETE MODEL THEORY
- 8.1 Introduction
- 8.2 Particles, Time, and Motion
- 8.3 Velocity and Acceleration
- 8.4 The Law of Motion
- 8.5 Damped Motion in a Nonlinear Force Field
- 8.6 Conservation of Energy
- 8.7 Nonlinear String Vibrations
- Exercises
- APPENDIX A: MATHEMATICS, THE EXACT SCIENCE
- APPENDIX B: FORTRAN PROGRAM NAVSTK
- REFERENCES AND SOURCES FOR FURTHER READING
- ANSWERS TO SELECTED EXERCISES
- Subject Index
