Discrete Numerical Methods in Physics and Engineering

Name: Discrete Numerical Methods in Physics and Engineering
Brand: Academic Press
Price: 77.95 EUR
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Greenspan(Autor*in)

Greenspan(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

325 Seiten

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978-0-08-095616-9 (ISBN)

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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

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