## Solving parabolic stochastic partial differential equations via averaging over characteristics

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- by G. N. Milstein and M. V. Tretyakov PDF
- Math. Comp.
**78**(2009), 2075-2106 Request permission

## Abstract:

The method of characteristics (the averaging over the characteristic formula) and the weak-sense numerical integration of ordinary stochastic differential equations together with the Monte Carlo technique are used to propose numerical methods for linear stochastic partial differential equations (SPDEs). Their orders of convergence in the mean-square sense and in the sense of almost sure convergence are obtained. A variance reduction technique for the Monte Carlo procedures is considered. Layer methods for linear and semilinear SPDEs are constructed and the corresponding convergence theorems are proved. The approach developed is supported by numerical experiments.## References

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## Additional Information

**G. N. Milstein**- Affiliation: Ural State University, Lenin Str. 51, 620083 Ekaterinburg, Russia
- Email: Grigori.Milstein@usu.ru
**M. V. Tretyakov**- Affiliation: Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdom
- Email: M.Tretyakov@le.ac.uk
- Received by editor(s): May 30, 2007
- Received by editor(s) in revised form: November 3, 2008
- Published electronically: March 6, 2009
- © Copyright 2009 American Mathematical Society
- Journal: Math. Comp.
**78**(2009), 2075-2106 - MSC (2000): Primary 65C30, 60H15, 60H35, 60G35
- DOI: https://doi.org/10.1090/S0025-5718-09-02250-9
- MathSciNet review: 2521279