Basic Concepts in Computational Physics

by Benjamin A. Stickler, Ewald Schachinger

Overview

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 shastic 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 shastics, and subsequently introduces Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. The final two chapters discuss data analysis and shastic optimization. All this is again motivated and augmented by applications from physics. Inaddition, 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.

Product Details

ISBN-13:	9783319272634
Publisher:	Springer International Publishing
Publication date:	03/22/2016
Edition description:	2nd ed. 2016
Pages:	409
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Ewald Schachinger
Institut für Theoretische und Computational Physik,
Technische Universität Graz, Petersgasse 16, A-8010 Graz [e-mail]

Benjamin A. Stickler
Institut für Theoretische Physik, Karl Franzens Universität
Graz, Universitätsplatz 5, A-8010 Graz, [e-mail]

Table of Contents

Some Basic Remarks.- Part I Deterministic Methods.- Numerical Differentiation.- Numerical Integration.- The KEPLER Problem.- Ordinary Differential Equations – Initial Value Problems.- The Double Pendulum.- Molecular Dynamics.- Numerics of Ordinary Differential Equations - Boundary Value Problems.- The One-Dimensional Stationary Heat Equation.- The One-Dimensional Stationary SCHRÖDINGER Equation.- Partial Differential Equations.- Part II Shastic Methods.- Pseudo Random Number Generators.- Random Sampling Methods.- A Brief Introduction to Monte-Carlo Methods.- The ISING Model.- Some Basics of Shastic Processes.- The Random Walk and Diffusion Theory.- MARKOV-Chain Monte Carlo and the POTTS Model.- Data Analysis.- Shastic Optimization.- Appendix: The Two-Body Problem.- Solving Non-Linear Equations. The NEWTON Method.- Numerical Solution of Systems of Equations.- Fast Fourier Transform.- Basics of Probability Theory.- Phase Transitions.- Fractional Integrals and Derivatives in1D.- Least Squares Fit.- Deterministic Optimization.

Editorial Reviews

From the reviews:

“The authors characterize the aim of their book to ‘address the scenarios of direct simulation of physical processes and the solution of complex mathematical problems on a very basic level’. It is directed to lecturers teaching basic courses in Computational Physics and to students as a companion when starting studying in this field.” (Rolf Dieter Grigorieff, zbMATH, Vol. 1287, 2014)

From the Publisher