Stochastic Numerical Methods (eBook)

Raul Toral is head of the department of Complex Systems at IFISC (Palma de Mallorca, Spain). He obtained his academic degrees from Barcelona university (Spain), spent two years at THE Physics Department of Edinburgh University (UK), and two more years at Lehigh University (Pennsylvania, USA), before joining the University of Balearic Islands where he has been a full professor since 1994. Prof. Toral has authored 200 scientific publications. He was the director of the Physbio International Summer School on Stochastic Processes in Biology held in St. Etienne de Tinnée (France) in 2006, and a member of the editorial board of Fluctuations and Noise Letters (2005-2007), as well as the organizer of several conferences devoted to basic issues and applications of Nonlinear and Statistical Physics. Pere Colet is Research Professor at IFISC (CSIC-UIB). He obtained his M.Sc. degree in physics from Universitat de Barcelona (1987) and his Ph. D. also in Physics from Universitat de les Illes Balears (1991), Spain. He was a postdoctoral Fulbright fellow at the School of Physics of the Georgia Institute of Tecnology. In May 1995, he joined the Spanish Consejo Superior de Investigaciones Cientificas. He has co-authored over 100 papers in ISI journals as well as 35 other scientific publications. His research interests include fluctuations and nonlinear dynamics of semiconductor lasers, synchronization of chaotic lasers and encoded communications, synchronization of coupled nonlinear oscillators, pattern formation, and quantum fluctuations in nonlinear optical cavities and dynamics of dissipative solitons.

1. Review of Probability Concepts
2. Monte Carlo Integration
3. Generation of Non-uniform Random Numbers: Non-correlated Values
4. Dynamical Methods
5. Applications to Statistical Mechanics
6. Introduction to Stochastic Processes
7. Numerical Simulation of Stochastic Differential
equations
8.Introduction to Master Equations
9. Numerical Simulations of Master Equations
10. Hybrid Monte Carlo
11. Stochastic Partial Differential Equations
A. Generation of Uniform ^U (0; 1) Random Numbers
B. Generation of n-dimensional Correlated Gaussian
Variables
C. Calculation of the Correlation Function of a Series
D. Collective Algorithms for Spin Systems
E. Histogram Extrapolation
F. Multicanonical Simulations
G. Discrete Fourier Transform