The ability of numerical methods to reproduce long-time features of a linear stochastic oscillator is examined. It is shown that certain, widely-used, methods fail to capture the correct second moment growth rate, whereas a customized extension of the partitioned Euler method behaves well in this respect. It is also shown that the partitioned Euler method inherits an infinite-oscillation property. A weaker oscillation result is proved for a wide class of numerical methods.
- numerical methods
- linear stochastic oscillator
- Euler method
Strømmen Melbø, A. H., & Higham, D. J. (2004). Numerical simulation of a linear stochastic oscillator with additive noise. Applied Numerical Mathematics, 51(1), 89-99. https://doi.org/10.1016/j.apnum.2004.02.003