Computational Physics

An Introduction

By: Franz J. Vesely

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Hardcover | 30 September 2001 | Edition Number 2

At a Glance

Hardcover
284 Pages

Edition Type
Revised

Dimensions(cm)
24.77 x 17.15 x 2.54

Hardcover

$169.75

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In a rapidly evolving field such as computational physics, six years is an eternity. Even though many of the elementary techniques described here are of venerable age, their assembly into sophisticated combined methods and their intensive application to ever new problems is an ongoing and exciting process. After six years, a new the new vistas edition of this textbook must therefore take into account some of that have opened up recently. Apart from these additions and some didactic improvements, the general struc ture of the book holds good. The first three chapters are devoted to a thorough, if concise, treatment of the main ingredients from numerical mathematics: finite differences, linear algebra, and stochastics. This exercise will prove valuable when we proceed, in chapters 4 and 5, to combine these elementary tools into powerful instruments for the integration of differential equations. The final chapters are devoted to a number of applications in selected fields: statistical physics, quantum mechanics, and hydrodynamics. I will gradually augment this text by web-resident sample programs. These will be written in JAVA and will be accompanied by short explanations and references to this text. Thus it may prove worthwhile to pay an occasional visit to my web-site www.ap.univie.ac.at/users/Franz.Vesely/ to see if any new applets have sprung up.

Industry Reviews

about the first edition:
`... a concise introduction to the methods and algorithms used in computational physics...clear in its presentation... useful for those beginning more advanced work in the field...'

From the reviews of the second edition:

"The book is an excellent introduction to computational physics. ... The book can be useful for graduate students of physical and mathematical faculties as well as for specialists in the field of numerical mathematics and mathematical modeling." (Piotr Matus, Zentralblatt MATH, Vol. 1049 (24), 2004)

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You Can Find This Book In

Non-Fiction Science Physics Mathematical Physics Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Numerical Analysis Applied Physics Computing & I.T.Computer Science Applied Mathematics

Computer Programming & Software Development Algorithms & Data Structures

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Paperback

Published: 27th September 2012

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The Three Pillars of Computational Physics	p. 1
Finite Differences	p. 7
Interpolation Formulae	p. 9
NGF Interpolation	p. 9
NGB Interpolation	p. 10
ST Interpolation	p. 11
Difference Quotients	p. 12
DNGF Formulae	p. 12
DNGB Formulae	p. 14
DST Formulae	p. 15
Finite Differences in Two Dimensions	p. 17
Sample Applications	p. 18
Classical Point Mechanics	p. 18
Diffusion and Thermal Conduction	p. 19
Linear Algebra	p. 21
Exact Methods	p. 22
Gauss Elimination and Back Substitution	p. 22
Simplifying Matrices: The Householder Transformation	p. 25
LU Decomposition	p. 26
Tridiagonal Matrices: Recursion Method	p. 29
Iterative Methods	p. 31
Jacobi Relaxation	p. 32
Gauss-Seidel Relaxation (GSR)	p. 34
Successive Over-Relaxation (SOR)	p. 34
Alternating Direction Implicit Method (ADI)	p. 36
Conjugate Gradient Method (CG)	p. 36
Eigenvalues and Eigenvectors	p. 40
Largest Eigenvalue and Related Eigenvector	p. 40
Arbitrary Eigenvalue/-vector: Inverse Iteration	p. 42
Sample Applications	p. 43
Diffusion and Thermal Conduction	p. 43
Potential Equation	p. 44
Electronic Orbitals	p. 45
Stochastics	p. 47
Equidistributed Random Variates	p. 49
Linear Congruential Generators	p. 49
Shift Register Generators	p. 50
Other Distributions	p. 53
Fundamentals	p. 53
Transformation Method	p. 56
Generalized Transformation Method	p. 57
Rejection Method	p. 59
Multivariate Gaussian Distribution	p. 62
Equidistribution in Orientation Space	p. 66
Random Sequences	p. 68
Fundamentals	p. 68
Markov Processes	p. 71
Autoregressive Processes	p. 74
Wiener-Levy Process	p. 77
Markov Chains and the Monte Carlo method	p. 78
Stochastic Optimization	p. 80
Simulated Annealing	p. 81
Genetic Algorithms	p. 82
Everything Flows	p. 85
Ordinary Differential Equations	p. 89
Initial Value Problems of First Order	p. 90
Euler-Cauchy Algorithm	p. 90
Stability and Accuracy of Difference Schemes	p. 91
Explicit Methods	p. 94
Implicit Methods	p. 96
Predictor-Corrector Method	p. 98
Runge-Kutta Method	p. 101
Extrapolation Method	p. 104
Initial Value Problems of Second Order	p. 105
Verlet Method	p. 105
Predictor-Corrector Method	p. 108
Nordsieck Formulation of the PC Method	p. 110
Runge-Kutta Method	p. 112
Symplectic Algorithms	p. 112
Numerov's Method	p. 117
Boundary Value Problems	p. 119
Shooting Method	p. 120
Relaxation Method	p. 121
Partial Differential Equations	p. 125
Initial Value Problems I (Hyperbolic)	p. 129
FTCS Scheme; Stability Analysis	p. 129
Lax Scheme	p. 131
Leapfrog Scheme (LF)	p. 133
Lax-Wendroff Scheme (LW)	p. 135
Lax and Lax-Wendroff in Two Dimensions	p. 135
Initial Value Problems II (Parabolic)	p. 138
FTCS Scheme	p. 138
Implicit Scheme of First Order	p. 140
Crank-Nicholson Scheme (CN)	p. 141
Dufort-Frankel Scheme (DF)	p. 143
Boundary Value Problems: Elliptic DE	p. 143
Relaxation and Multigrid Techniques	p. 147
ADI Method for the Potential Equation	p. 148
Fourier Transform Method (FT)	p. 150
Cyclic Reduction (CR)	p. 153
Anchors Aweigh	p. 157
Simulation and Statistical Mechanics	p. 161
Model Systems of Statistical Mechanics	p. 164
A Nutshellfull of Fluids and Solids	p. 164
Tricks of the Trade	p. 168
Monte Carlo Method	p. 171
Molecular Dynamics Simulation	p. 175
Hard Spheres	p. 175
Continuous Potentials	p. 177
Beyond Basic Molecular Dynamics	p. 178
Evaluation of Simulation Experiments	p. 181
Pair Correlation Function	p. 182
Autocorrelation Functions	p. 184
Particles and Fields	p. 185
Ewald summation	p. 186
Particle-Mesh Methods (PM and P3M)	p. 188
Stochastic Dynamics	p. 191
Quantum Mechanical Simulation	p. 195
Diffusion Monte Carlo (DMC)	p. 196
Path Integral Monte Carlo (PIMC)	p. 201
Wave Packet Dynamics (WPD)	p. 209
Density Functional Molecular Dynamics (DFMD)	p. 211
Hydrodynamics	p. 215
Compressible Flow without Viscosity	p. 216
Explicit Eulerian Methods	p. 217
Particle-in-Cell Method (PIC)	p. 218
Smoothed Particle Hydrodynamics (SPH)	p. 220
Incompressible Flow with Viscosity	p. 226
Vorticity Method	p. 227
Pressure Method	p. 229
Free Surfaces: Marker-and-Cell Method (MAC)	p. 231
Lattice Gas Models for Hydrodynamics	p. 232
Lattice Gas Cellular Automata	p. 232
The Lattice Boltzmann Method	p. 236
Direct Simulation Monte Carlo / Bird method	p. 237
Appendixes	p. 239
Machine Errors	p. 241
Discrete Fourier Transformation	p. 245
Fundamentals	p. 245
Fast Fourier Transform (FFT)	p. 246
Bibliography	p. 249
Index	p. 257
Table of Contents provided by Syndetics. All Rights Reserved.

Computational Physics

An Introduction

At a Glance

Hardcover

Industry Reviews

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How to return your order

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You Can Find This Book In

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Paperback

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