On modified Crank-Nicholson difference schemes for stochastic parabolic equation

Numerical Functional Analysis and Optimization

Volumn 29, Issue 3-4, 2008, Pages 268-282

  Ashyralyev, A ^a,b  

^a FATIH UNIVERSITY   (Turkey)

^b Intl Turkmen Turkish University   (Turkmenistan)

Author keywords

Convergence; Difference schemes; Stochastic parabolic equation

Indexed keywords

BANACH SPACES; DIFFERENTIATION (CALCULUS); HILBERT SPACES; MATHEMATICAL OPERATORS; STANDARDS; STOCHASTIC PROGRAMMING; THEOREM PROVING;

(I ,J) CONDITIONS; (U ,V) OPERATOR; ADJOINT; APPROXIMATE SOLUTIONS; CAUCHY PROBLEMS; CONVERGENCE (MATHEMATICS); DIFFERENCE SCHEMES; HILBERT; INITIAL VALUES; NICHOLSON (CO); PARABOLIC EQUATION (PE); POSITIVE DEFINITE; PROBABILITY SPACES; WIENER PROCESSES;

DIFFERENCE EQUATIONS;

EID: 46249084133     PISSN: 01630563     EISSN: 15322467     Source Type: Journal    
DOI: 10.1080/01630560801998138     Document Type: Article

References (11)

1. E.J. Allen, S.J. Novosel, and Z. Zhang (1998). Finite element and difference approximation of some linear stochastic partial differential equations. Stochastics and Stochastics Reports 64:117-142.
2. A. Ashyralyev (1989). Estimation of the convergence of modified Crank-Nicholson difference schemes for parabolic equations with nonsmooth imput data. Izv. Akad. Nauk Turkmen. SSR Ser. Fiz. -Tekhn. Khim. Geol. Nauk 1:3-8 [Russian].
3. A. Ashyralyev and I. Hasgur (1995). Linear stochastic differential equations in a Hilbert space. Abs. of Statistic Conference-95, Dovlet Statistic Institute Publishing, Ankara, Turkey, p. 6
4. A. Ashyralyev and G. Michaletsky (1993). The approximation of solutions of stochastic differential equations in Hilbert space by the difference schemes. Trudy nauchno-prakticheskoy konferencii "Differencialniye uravneniya i ih prilozheniya", Ilim, Ashgabat, 1, pp. 85-95.
5. A. Ashyralyev and P.E. Sobolevskii (2004). New Difference Schemes for Partial Differential Equations. Operator Theory and Appl., Birkhäuser Verlag, Basel, Boston, Berlin, p. 148.
6. R.F. Curtain and P.L. Falb (1971). Stochastic differential equations in Hilbert spaces. J. Differential Equations 10:412-430.
7. E. Hausenblas (2002). Numerical analysis of semilinear stochastic evolution equations in Banach spaces. J. Computat. Appl. Math. 147:485-516.
8. G. Da Prato (1982). Regularity properties of a stochastic convolution integral. Atti Acc. Naz. Lincey 72(4):217-219.
9. G. Da Prato and J. Zabczyk (1992). Stochastic equations in infinite dimensions. Encyclopedia of Mathematics and its Applications. Vol. 44. Cambridge University Press, Cambridge.
10. T. Shardlow (1999). Numerical methods for stochastic parabolic PDEs. Numer. Funct. Anal. Optim. 20:121-145.
11. A. Yurtsever and A. Yazliyev (2000). High order accuracy difference scheme for stochastic parabolic equation in a Hilbert space. Some Problems of Applied Mathematics. Fatih University, Istanbul, pp. 212-220.