Overview
- Deterministic methods are presented on a par with stochastic methods
- Mathematically precise, but driven by the needs of physicists
- Covers modern applications
- Extensive appendices deepen the knowledge and present the mathematical basis
- Includes supplementary material: sn.pub/extras
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Table of contents (20 chapters)
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Front Matter
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Deterministic Methods
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Front Matter
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Keywords
About this book
- 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.
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)Authors and Affiliations
About the authors
Institut für Theoretische und Computational Physik,
Technische Universität Graz, Petersgasse 16, A-8010 Graz
schachinger@itp.tugraz.ac.at
Benjamin A. Stickler
Institut für Theoretische Physik, Karl Franzens Universität
Graz, Universitätsplatz 5, A-8010 Graz, benjamin.stickler@uni-graz.at
Bibliographic Information
Book Title: Basic Concepts in Computational Physics
Authors: Benjamin A. Stickler, Ewald Schachinger
DOI: https://doi.org/10.1007/978-3-319-02435-6
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Nature Switzerland AG 2014
Edition Number: 1
Number of Pages: XVII, 377
Number of Illustrations: 95 b/w illustrations
Topics: Numerical and Computational Physics, Simulation, Mathematical and Computational Engineering, Computational Mathematics and Numerical Analysis, Theoretical and Computational Chemistry, Complex Systems, Statistical Physics and Dynamical Systems