Stochastic numerical methods

The book introduces at a master's level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. The authors develop in detail examples from the phase-transitions field to explain the whole process from the numerical simulation (design of the convenient algorithm) to the data analysis (extraction of critical exponents, finite-size effects, etc). The core of the book covers Monte Carlo type methods with applications to statistical physics and phase transitions, numerical methods for stochastic differential equations - both ordinary and partial (including advanced pseudo-spectral methods-, Gillespie's method to simulate the dynamics of systems described by master equations (e. g. birth and death processes, and applications to Biology, such as protein expression and transcription). Finally, and in order to explain modern hybrid algorithms (combining Monte Carlo and stochastic differential equations), the authors explain the basics of molecular dynamics. Appendices with supplementary material for more advanced topics, end-of-chapter practical exercises, and useful codes for the core methods are included.