The Three Pillars of Computational Physics / I: |
Finite Differences / 1: |
Interpolation Formulae / 1.1: |
NGF Interpolation / 1.1.1: |
NGB Interpolation / 1.1.2: |
ST Interpolation / 1.1.3: |
Difference Quotients / 1.2: |
DNGF Formulae / 1.2.1: |
DNGB Formulae / 1.2.2: |
DST Formulae / 1.2.3: |
Finite Differences in Two Dimensions / 1.3: |
Sample Applications / 1.4: |
Classical Point Mechanics / 1.4.1: |
Diffusion and Thermal Conduction / 1.4.2: |
Linear Algebra / 2: |
Exact Methods / 2.1: |
Gauss Elimination and Back Substitution / 2.1.1: |
Simplifying Matrices: The Householder Transformation / 2.1.2: |
LU Decomposition / 2.1.3: |
Tridiagonal Matrices: Recursion Method / 2.1.4: |
Iterative Methods / 2.2: |
Jacobi Relaxation / 2.2.1: |
Gauss-Seidel Relaxation (GSR) / 2.2.2: |
Successive Over-Relaxation (SOR) / 2.2.3: |
Alternating Direction Implicit Method (ADI) / 2.2.4: |
Conjugate Gradient Method (CG) / 2.2.5: |
Eigenvalues and Eigenvectors / 2.3: |
Largest Eigenvalue and Related Eigenvector / 2.3.1: |
Arbitrary Eigenvalue/-vector: Inverse Iteration / 2.3.2: |
Potential Equation / 2.4: |
Electronic Orbitals / 2.4.3: |
Stochastics / 3: |
Equidistributed Random Variates / 3.1: |
Linear Congruential Generators / 3.1.1: |
Shift Register Generators / 3.1.2: |
Other Distributions / 3.2: |
Fundamentals / 3.2.1: |
Transformation Method / 3.2.2: |
Generalized Transformation Method / 3.2.3: |
Rejection Method / 3.2.4: |
Multivariate Gaussian Distribution / 3.2.5: |
Equidistribution in Orientation Space / 3.2.6: |
Random Sequences / 3.3: |
Markov Processes / 3.3.1: |
Autoregressive Processes / 3.3.3: |
Wiener-Levy Process / 3.3.4: |
Markov Chains and the Monte Carlo method / 3.3.5: |
Stochastic Optimization / 3.4: |
Simulated Annealing / 3.4.1: |
Genetic Algorithms / 3.4.2: |
Everything Flows / II: |
Ordinary Differential Equations / 4: |
Initial Value Problems of First Order / 4.1: |
Euler-Cauchy Algorithm / 4.1.1: |
Stability and Accuracy of Difference Schemes / 4.1.2: |
Explicit Methods / 4.1.3: |
Implicit Methods / 4.1.4: |
Predictor-Corrector Method / 4.1.5: |
Runge-Kutta Method / 4.1.6: |
Extrapolation Method / 4.1.7: |
Initial Value Problems of Second Order / 4.2: |
Verlet Method / 4.2.1: |
Nordsieck Formulation of the PC Method / 4.2.2: |
Symplectic Algorithms / 4.2.4: |
Numerov's Method / 4.2.6: |
Boundary Value Problems / 4.3: |
Shooting Method / 4.3.1: |
Relaxation Method / 4.3.2: |
Partial Differential Equations / 5: |
Initial Value Problems I (Hyperbolic) / 5.1: |
FTCS Scheme; Stability Analysis / 5.1.1: |
Lax Scheme / 5.1.2: |
Leapfrog Scheme (LF) / 5.1.3: |
Lax-Wendroff Scheme (LW) / 5.1.4: |
Lax and Lax-Wendroff in Two Dimensions / 5.1.5: |
Initial Value Problems II (Parabolic) / 5.2: |
FTCS Scheme / 5.2.1: |
Implicit Scheme of First Order / 5.2.2: |
Crank-Nicholson Scheme (CN) / 5.2.3: |
Dufort-Frankel Scheme (DF) / 5.2.4: |
Boundary Value Problems: Elliptic DE / 5.3: |
Relaxation and Multigrid Techniques / 5.3.1: |
ADI Method for the Potential Equation / 5.3.2: |
Fourier Transform Method (FT) / 5.3.3: |
Cyclic Reduction (CR) / 5.3.4: |
Anchors Aweigh / III: |
Simulation and Statistical Mechanics / 6: |
Model Systems of Statistical Mechanics / 6.1: |
A Nutshellfull of Fluids and Solids / 6.1.1: |
Tricks of the Trade / 6.1.2: |
Monte Carlo Method / 6.2: |
Molecular Dynamics Simulation / 6.3: |
Hard Spheres / 6.3.1: |
Continuous Potentials / 6.3.2: |
Beyond Basic Molecular Dynamics / 6.3.3: |
Evaluation of Simulation Experiments / 6.4: |
Pair Correlation Function / 6.4.1: |
Autocorrelation Functions / 6.4.2: |
Particles and Fields / 6.5: |
Ewald summation / 6.5.1: |
Particle-Mesh Methods (PM and P3M) / 6.5.2: |
Stochastic Dynamics / 6.6: |
Quantum Mechanical Simulation / 7: |
Diffusion Monte Carlo (DMC) / 7.1: |
Path Integral Monte Carlo (PIMC) / 7.2: |
Wave Packet Dynamics (WPD) / 7.3: |
Density Functional Molecular Dynamics (DFMD) / 7.4: |
Hydrodynamics / 8: |
Compressible Flow without Viscosity / 8.1: |
Explicit Eulerian Methods / 8.1.1: |
Particle-in-Cell Method (PIC) / 8.1.2: |
Smoothed Particle Hydrodynamics (SPH) / 8.1.3: |
Incompressible Flow with Viscosity / 8.2: |
Vorticity Method / 8.2.1: |
Pressure Method / 8.2.2: |
Free Surfaces: Marker-and-Cell Method (MAC) / 8.2.3: |
Lattice Gas Models for Hydrodynamics / 8.3: |
Lattice Gas Cellular Automata / 8.3.1: |
The Lattice Boltzmann Method / 8.3.2: |
Direct Simulation Monte Carlo / Bird method / 8.4: |
Appendixes |
Machine Errors / A: |
Discrete Fourier Transformation / B: |
Fast Fourier Transform (FFT) / B.1: |
Bibliography |
Index |
The Three Pillars of Computational Physics / I: |
Finite Differences / 1: |
Interpolation Formulae / 1.1: |