## Basic Concepts in Computational PhysicsWith the development of ever more powerful computers a new branch of physics and engineering evolved over the last few decades: Computer Simulation or Computational Physics. It serves two main purposes: - Solution of complex mathematical problems such as, differential equations, minimization/optimization, or high-dimensional sums/integrals. - Direct simulation of physical processes, as for instance, molecular dynamics or Monte-Carlo simulation of physical/chemical/technical processes. Consequently, the book is divided into two main parts: Deterministic methods and stochastic methods. Based on concrete problems, the first part discusses numerical differentiation and integration, and the treatment of ordinary differential equations. This is augmented by notes on the numerics of partial differential equations. The second part discusses the generation of random numbers, summarizes the basics of stochastics which is then followed by the introduction of various Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. All this is again augmented by numerous applications from physics. The final two chapters on Data Analysis and Stochastic Optimization share the two main topics as a common denominator. The book offers a number of appendices to provide the reader with more detailed information on various topics discussed in the main part. Nevertheless, the reader should be familiar with the most important concepts of statistics and probability theory albeit two appendices have been dedicated to provide a rudimentary discussion. |

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### Contents

1 Some Basic Remarks | 1 |

Part I Deterministic Methods
| 14 |

2 Numerical Differentiation | 17 |

3 Numerical Integration | 29 |

4 The KEPLER Problem | 51 |

Initial Value Problems | 60 |

6 The Double Pendulum | 81 |

7 Molecular Dynamics | 97 |

15 The ISING Model | 209 |

16 Some Basics of Stochastic Processes | 229 |

17 The Random Walk and Diffusion Theory | 251 |

18 MarkovChain Monte Carlo and the Potts Model | 275 |

19 Data Analysis | 287 |

20 Stochastic Optimization | 298 |

Appendix A The TwoBody Problem
| 315 |

The Newton Method
| 321 |

Boundary Value Problems | 110 |

9 The OneDimensional Stationary Heat Equation | 123 |

10 The OneDimensional Stationary Schrödinger Equation | 131 |

11 Partial Differential Equations | 147 |

Part II Stochastic Methods
| 169 |

12 Pseudo Random Number Generators | 170 |

13 Random Sampling Methods | 185 |

14 A Brief Introduction to MonteCarlo Methods | 196 |

### Other editions - View all

Basic Concepts in Computational Physics Benjamin a Stickler,Ewald Schachinger No preview available - 2018 |

Basic Concepts in Computational Physics Benjamin A. Stickler,Ewald Schachinger No preview available - 2016 |

### Common terms and phrases

analytically approximation arbitrary B. A. Stickler boundary conditions boundary value problem calculate Chap chapter Computational Physics Concepts in Computational configuration defined denotes detailed balance difference derivative diffusion eigenvalue energy error Euler method expectation value explicit Euler finite difference function f(x function values Furthermore grid-points Hence illustrated implicit Euler method initial conditions instance International Publishing Switzerland interval introduced Ising model iteration Let us briefly Lévy flight linear linear congruential magnetization Markov-chain Monte Carlo matrix Metropolis algorithm numerical solution obtain parameters particle particular polynomial potential Potts model probability Publishing Switzerland 2014 random numbers random variables random walk rectangular rule referred sampling Schachinger second order sequence simulation solve space spin Springer International Publishing step stochastic process symplectic temperature trajectory variance vector velocity Wiener process yn+1