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Computational Physics An Introduction

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ISBN-10: 0306466317

ISBN-13: 9780306466311

Edition: 2nd 2001 (Revised)

Authors: Franz J. Vesely

List price: $169.99
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The essential point in computational physics is not the use of machines, but the systematic application of numerical techniques in place of, and in addition to, analytical methods, in order to render accessible to computation as large a part of physical reality as possible. The various available techniques, disparate as they may seem, are traced back to only three main methodological sources; finite difference calculus, linear algebra, and stochastics. Each algorithm is carefully introduced and every computational tool is explained in terms of fundamental numerical techniques. Examples from statistical mechanics, quantum mechanics, and hydrodynamics are employed to bridge the gap between…    
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Book details

List price: $169.99
Edition: 2nd
Copyright year: 2001
Publisher: Springer
Publication date: 9/30/2001
Binding: Hardcover
Pages: 259
Size: 6.75" wide x 9.75" long x 1.00" tall
Weight: 1.628
Language: English

The Three Pillars of Computational Physics
Finite Differences
Interpolation Formulae
NGF Interpolation
NGB Interpolation
ST Interpolation
Difference Quotients
DNGF Formulae
DNGB Formulae
DST Formulae
Finite Differences in Two Dimensions
Sample Applications
Classical Point Mechanics
Diffusion and Thermal Conduction
Linear Algebra
Exact Methods
Gauss Elimination and Back Substitution
Simplifying Matrices: The Householder Transformation
LU Decomposition
Tridiagonal Matrices: Recursion Method
Iterative Methods
Jacobi Relaxation
Gauss-Seidel Relaxation (GSR)
Successive Over-Relaxation (SOR)
Alternating Direction Implicit Method (ADI)
Conjugate Gradient Method (CG)
Eigenvalues and Eigenvectors
Largest Eigenvalue and Related Eigenvector
Arbitrary Eigenvalue/-vector: Inverse Iteration
Sample Applications
Diffusion and Thermal Conduction
Potential Equation
Electronic Orbitals
Equidistributed Random Variates
Linear Congruential Generators
Shift Register Generators
Other Distributions
Transformation Method
Generalized Transformation Method
Rejection Method
Multivariate Gaussian Distribution
Equidistribution in Orientation Space
Random Sequences
Markov Processes
Autoregressive Processes
Wiener-Levy Process
Markov Chains and the Monte Carlo method
Stochastic Optimization
Simulated Annealing
Genetic Algorithms
Everything Flows
Ordinary Differential Equations
Initial Value Problems of First Order
Euler-Cauchy Algorithm
Stability and Accuracy of Difference Schemes
Explicit Methods
Implicit Methods
Predictor-Corrector Method
Runge-Kutta Method
Extrapolation Method
Initial Value Problems of Second Order
Verlet Method
Predictor-Corrector Method
Nordsieck Formulation of the PC Method
Runge-Kutta Method
Symplectic Algorithms
Numerov's Method
Boundary Value Problems
Shooting Method
Relaxation Method
Partial Differential Equations
Initial Value Problems I (Hyperbolic)
FTCS Scheme; Stability Analysis
Lax Scheme
Leapfrog Scheme (LF)
Lax-Wendroff Scheme (LW)
Lax and Lax-Wendroff in Two Dimensions
Initial Value Problems II (Parabolic)
FTCS Scheme
Implicit Scheme of First Order
Crank-Nicholson Scheme (CN)
Dufort-Frankel Scheme (DF)
Boundary Value Problems: Elliptic DE
Relaxation and Multigrid Techniques
ADI Method for the Potential Equation
Fourier Transform Method (FT)
Cyclic Reduction (CR)
Anchors Aweigh
Simulation and Statistical Mechanics
Model Systems of Statistical Mechanics
A Nutshellfull of Fluids and Solids
Tricks of the Trade
Monte Carlo Method
Molecular Dynamics Simulation
Hard Spheres
Continuous Potentials
Beyond Basic Molecular Dynamics
Evaluation of Simulation Experiments
Pair Correlation Function
Autocorrelation Functions
Particles and Fields
Ewald summation
Particle-Mesh Methods (PM and P3M)
Stochastic Dynamics
Quantum Mechanical Simulation
Diffusion Monte Carlo (DMC)
Path Integral Monte Carlo (PIMC)
Wave Packet Dynamics (WPD)
Density Functional Molecular Dynamics (DFMD)
Compressible Flow without Viscosity
Explicit Eulerian Methods
Particle-in-Cell Method (PIC)
Smoothed Particle Hydrodynamics (SPH)
Incompressible Flow with Viscosity
Vorticity Method
Pressure Method
Free Surfaces: Marker-and-Cell Method (MAC)
Lattice Gas Models for Hydrodynamics
Lattice Gas Cellular Automata
The Lattice Boltzmann Method
Direct Simulation Monte Carlo / Bird method
Machine Errors
Discrete Fourier Transformation
Fast Fourier Transform (FFT)