An approximation of semigroups method for stochastic parabolic equations. (English) Zbl 1259.65003

Ashyralyev, Allaberen; San, Mehmet Emin

Abstr. Appl. Anal. 2012, Article ID 684248, 24 p. (2012).

Summary: A single-step difference scheme for the numerical solution of the nonlocal-boundary value problem for stochastic parabolic equations is presented. The convergence estimate for the solution of the difference scheme is established. In application, the convergence estimates for the solution of the difference scheme are obtained for two nonlocal-boundary value problems. The theoretical statements for the solution of this difference scheme are supported by numerical examples.

MSC:

65C30	Numerical solutions to stochastic differential and integral equations
60H15	Stochastic partial differential equations (aspects of stochastic analysis)
60H35	Computational methods for stochastic equations (aspects of stochastic analysis)
35R60	PDEs with randomness, stochastic partial differential equations
35K10	Second-order parabolic equations
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

single-step difference scheme; nonlocal-boundary value problem; stochastic parabolic equations; convergence; numerical examples

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