Stochastic simulation methods



  1. Monte Carlo integration: Problems in one variable. Statistical errors. Generation of random numbers.
  2. Monte Carlo integration in many variables: Metropolis and thermal bath.
  3. Collective algorithms for Ising and Potts models.
  4. Extrapolation techniques: Ferrenberg-Swendsen algorithm.
  5. Applications to phase transitions: critical phenomena, analysis in terms of finite size scaling.
  6. Main algorithms for the integration of stochastic differential equations: Euler, Milshtein and Heun methods.
  7. Numerical integration of partial differential equations: finite differences, pseudospectral methods, stochastic equations.
  8. Molecular dynamics. Temporal reversibility and symplectic algorithms. Hybrid Monte Carlo.
  9. Numerical simulation of master equations. First reaction and residence time algorithms.