<p>With 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:<br>- Solution of complex mathematical problems such as, differential equations, minimization/o
Basic Concepts in Computational Physics
β Scribed by Benjamin A. Stickler, Ewald Schachinger (auth.)
- Publisher
- Springer International Publishing
- Year
- 2016
- Tongue
- English
- Leaves
- 412
- Edition
- 2
- Category
- Library
No coin nor oath required. For personal study only.
β¦ Synopsis
This new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for the direct simulation of physical processes.
The book is divided into two main parts: Deterministic methods and stochastic methods in computational physics. Based on concrete problems, the first part discusses numerical differentiation and integration, as well as the treatment of ordinary differential equations. This is extended by a brief introduction to the numerics of partial differential equations. The second part deals with the generation of random numbers, summarizes the basics of stochastics, and subsequently introduces Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. The final two chapters discuss data analysis and stochastic optimization. All this is again motivated and augmented by applications from physics. In addition, the book offers a number of appendices to provide the reader with information on topics not discussed in the main text.
Numerous problems with worked-out solutions, chapter introductions and summaries, together with a clear and application-oriented style support the reader. Ready to use C++ codes are provided online.
β¦ Table of Contents
Front Matter....Pages i-xvi
Some Basic Remarks....Pages 1-13
Front Matter....Pages 15-15
Numerical Differentiation....Pages 17-30
Numerical Integration....Pages 31-52
The Kepler Problem....Pages 53-61
Ordinary Differential Equations: Initial Value Problems....Pages 63-83
The Double Pendulum....Pages 85-101
Molecular Dynamics....Pages 103-116
Numerics of Ordinary Differential Equations: Boundary Value Problems....Pages 117-129
The One-Dimensional Stationary Heat Equation....Pages 131-138
The One-Dimensional Stationary SchrΓΆdinger Equation....Pages 139-156
Partial Differential Equations....Pages 157-180
Front Matter....Pages 181-181
Pseudo-random Number Generators....Pages 183-195
Random Sampling Methods....Pages 197-209
A Brief Introduction to Monte-Carlo Methods....Pages 211-223
The Ising Model....Pages 225-246
Some Basics of Stochastic Processes....Pages 247-270
The Random Walk and Diffusion Theory....Pages 271-295
Markov-Chain Monte Carlo and the Potts Model....Pages 297-310
Data Analysis....Pages 311-321
Stochastic Optimization....Pages 323-339
Back Matter....Pages 341-409
β¦ Subjects
Numerical and Computational Physics;Appl.Mathematics/Computational Methods of Engineering;Computational Mathematics and Numerical Analysis;Theoretical and Computational Chemistry
π SIMILAR VOLUMES
This new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for the direct simulation of physical processes. The book is divided into two main parts: Deterministic meth
This new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for the direct simulation of physical processes.<br /><br />The book is divided into two main parts: Determi