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Discrete numerical methods in physics and engineering
1 online resource (xi, 312 pages) : illustrations
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 Equation2.8 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 Dimensions3.10 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 Problems5.6 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 Problems7.4 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
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
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Includes bibliographical references (pages 292-304) and index.
Mathematics in science and engineering ; v. 107