On Modified Crank–Nicholson Difference Schemes for Stochastic Parabolic Equation
Allaberen Ashyralyev
Department of Mathematics, Fatih University, Istanbul, Turkey;
International Turkmen-Turkish University, Ashgabat, Turkmenistan
2008en
ABI
Abstract
Abstract We consider the modified Crank–Nicholson difference schemes for the approximate solution of the initial value Cauchy problem for stochastic parabolic equation in a Hilbert space H with the self-adjoint positive definite operator A. Here: (1) w t is a standard Wiener process given on the probability space (Ω,F,P). (2) f(t) is an element of space that consists of H 1-value processes for which the condition is satisfied. The estimate of convergence for the solution of these difference schemes is obtained. Keywords: ConvergenceDifference schemesStochastic parabolic equationAMS Subject Classification: 60H1560J35
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