This new edition is a concise introduction tothe basic methods of computational physics. Readers will discover the benefits of numerical methodsfor solving complex mathematical problems and for the direct simulation of physical processes.The book is divided into two main parts: Deterministic methods and stochasticmethods in computational physics. Based on concrete problems, the firstpart discusses numerical differentiation and integration, as well as the treatment of ordinarydifferential equations. This is extended by a brief introduction to the numerics of partial differential equations. Thesecond part deals with the generation of random numbers, summarizes the basics of stochastics, andsubsequently introduces Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. Thefinal two chapters discuss data analysis and stochastic optimization. All this is again motivated andaugmented by applications from physics. In addition, the book offers a number of
appendices to provide thereader with information on topics not discussed in the main text.Numerous problems with worked-out solutions, chapter introductions andsummaries, together with a clear and application-oriented style support thereader. Ready to use C++ codes are provided online.
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 Stochastic Methods.- Pseudo Random Number Generators.- Random Sampling Methods.- A Brief Introduction to Monte-Carlo Methods.- The ISING Model.- Some Basics of Stochastic Processes.- The Random Walk and Diffusion Theory.- MARKOV-Chain Monte Carlo and the POTTS Model.- Data Analysis.- Stochastic 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 in
1D.- Least Squares Fit.- Deterministic Optimization.
