Approximation of stochastic parabolic differential equations with two different finite difference schemes. (English) Zbl 1260.60124

Soheili, A. R.; Niasar, M. B.; Arezoomandan, M.

Bull. Iran. Math. Soc. 37, No. 2, Part 1, 61-83 (2011).

Summary: We focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of ltô type, in particular, parabolic equations. The main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
60H35	Computational methods for stochastic equations (aspects of stochastic analysis)

Keywords:

stochastic partial differential equations; finite difference methods; Saul’yev methods; convergence; stability; Wiener process