Balanced implicit methods for stiff stochastic systems: An introduction and numerical experiments.
- Milstein, Grigori N.
- Platen, Eckhard
- Schurz, Henri
2010 Mathematics Subject Classification
- Stochastic differential equations, implicit numerical methods, stiff equations, simulation experiments
The paper introduces implicitness in stochastic terms of numerical methods for solving of stiff stochastic differential equations and especially a class of fully implicit methods, the balanced methods. Their order of strong convergence is proved. Systematic numerical experiments compare the numerical behaviour of these schemes with that of different other schemes. A wide class of model equations are also provided as one by-product in order to test numerical methods in the case of stochastic stiffness in the given system.