Content: Cover
Half Title
Title Page
Copyright Page
Preface
Preface to the FORTRAN Edition
How to use this book
Table of Contents
Chapter 1: Basic Mathematical Operations
1.1 Numerical differentiation
1.2 Numerical quadrature
1.3 Finding roots
1.4 Semiclassical quantization of molecular vibrations
Project I: Scattering by a central potential
Chapter 2: Ordinary Differential Equations
2.1 Simple methods
2.2 Multistep and implicit methods
2.3 Runge-Kutta methods
2.4 Stability
2.5 Order and chaos in two-dimensional motion
Project II: The structure of white dwarf stars. II. 1 The equations of equilibriumII. 2 The equation of state
II. 3 Scaling the equations
II. 4 Solving the equations
Chapter 3: Boundary Value and Eigenvalue Problems
3.1 The Numerov algorithm
3.2 Direct integration of boundary value problems
3.3 GreenaΜ#x80
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s function solution of boundary value problems
3.4 Eigenvalues of the wave equation
3.5 Stationary solutions of the one-dimensional Schroedinger equation
Project III: Atomic structure in the Hartree-Fock approximation
III. 1 Basis of the Hartree-Fock approximation
III. 2 The two-electron problem
III. 3 Many-electron systems. III. 4 Solving the equationsChapter 4: Special Functions and Gaussian Quadrature
4.1 Special functions
4.2 Gaussian quadrature
4.3 Born and eikonal approximations to quantum scattering
Project IV: Partial wave solution of quantum scattering
IV. 1 Partial wave decomposition of the wave function
IV. 2 Finding the phase shifts
IV. 3 Solving the equations
Chapter 5: Matrix Operations
5.1 Matrix inversion
5.2 Eigenvalues of a tri-diagonal matrix
5.3 Reduction to tri-diagonal form
5.4 Determining nuclear charge densities
Project V: A schematic shell model
V.1 Definition of the model. V.2 The exact eigenstatesV. 3 Approximate eigenstates
V.4 Solving the model
Chapter 6: Elliptic Partial Differential Equations
6.1 Discretization and the variational principle
6.2 An iterative method for boundary value problems
6.3 More on discretization
6.4 Elliptic equations in two dimensions
Project VI: Steady-state hydrodynamics in two dimensions
VI. 1 The equations and their discretization
VI. 2 Boundary conditions
VI. 3 Solving the equations
Chapter 7: Parabolic Partial Differential Equations
7.1 Naive discretization and instabilities. 7.2 Implicit schemes and the inversion of tri-diagonal matrices7.3 Diffusion and boundary value problems in two dimensions
7.4 Iterative methods for eigenvalue problems
7.5 The time-dependent Schroedinger equation
Project VII: Self-organization in chemical reactions
VII. 1 Description of the model
VII. 2 Linear stability analysis
VII. 3 Numerical solution of the model
Chapter 8: Monte Carlo Methods
8.1 The basic Monte Carlo strategy
8.2 Generating random variables with a specified distribution
8.3 The algorithm of Metropolis et al.,
8.4 The Ising model in two dimensions.