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