- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 684248, 24 pages
An Approximation of Semigroups Method for Stochastic Parabolic Equations
1Department of Mathematics, Fatih University, Buyukcekmece,
34500 Istanbul, Turkey
2Department of Mathematics, ITTU, 74012 Ashgabat, Turkmenistan
3Certified Dental Supply LLC 43 River Road, Nutley, NJ 07031, USA
Received 25 May 2012; Accepted 8 June 2012
Academic Editor: Ravshan Ashurov
Copyright © 2012 Allaberen Ashyralyev and Mehmet Emin San. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. Ashyralyev and I. Hasgur, “Linear stochastic differential equations in a Hilbert space,” Abstract of Statistic Conference-95, Ankara, Turkey, 1–6, 1995.
- R. F. Curtain and P. L. Falb, “Stochastic differential equations in Hilbert space,” Journal of Differential Equations, vol. 10, pp. 412–430, 1971.
- G. Da Prato, “Regularity properties of a stochastic convolution integral,” Analisi Matematica, vol. 72, no. 4, pp. 217–219, 1982.
- G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, vol. 44 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, UK, 1992.
- A. Ashyralyev and G. Michaletsky, “The approximation of solutions of stochastic differential equations in Hilbert space by the difference schemes, Trudy nauchno-prakticheskoy konferencii, ‘Differencialniye uravneniya i ih prilozheniya’,” Ashgabat, vol. 1, pp. 85–95, 1993.
- E. J. Allen, S. J. Novosel, and Z. Zhang, “Finite element and difference approximation of some linear stochastic partial differential equations,” Stochastics and Stochastics Reports, vol. 64, no. 1-2, pp. 117–142, 1998.
- E. Hausenblas, “Numerical analysis of semilinear stochastic evolution equations in Banach spaces,” Journal of Computational and Applied Mathematics, vol. 147, no. 2, pp. 485–516, 2002.
- A. Yurtsever and A. Yazliyev, “High order accuracy difference scheme for stochastic parabolic equation in a Hilbert space,” in Some Problems of Applied Mathematics, pp. 212–220, Fatih University, Istanbul, Turkey, 2000.
- T. Shardlow, “Numerical methods for stochastic parabolic PDEs,” Numerical Functional Analysis and Optimization, vol. 20, no. 1-2, pp. 121–145, 1999.
- A. Ashyralyev, “On modified Crank-Nicholson difference schemes for stochastic parabolic equation,” Numerical Functional Analysis and Optimization, vol. 29, no. 3-4, pp. 268–282, 2008.
- L. Han, L. G. Han, X. B. Gong, Shan Gang-Yi, and J. Cui, “Implicit finite-difference plane wave migration in TTI media,” Chinese Journal of Geophysics, vol. 54, no. 4, pp. 1090–1097, 2011.
- A. Jentzen, “Higher order pathwise numerical approximations of SPDEs with additive noise,” SIAM Journal on Numerical Analysis, vol. 49, no. 2, pp. 642–667, 2011.
- A. Jentzen and P. E. Kloeden, “The numerical approximation of stochastic partial differential equations,” Milan Journal of Mathematics, vol. 77, no. 1, pp. 205–244, 2009.
- A. Ashyralyev and M. Akat, “An approximation of stochastic hyperbolic equations,” AIP Conference Proceedings, vol. 1389, pp. 625–628, 2011.
- A. Ashyralyev and E. M. San, “Finite difference method for stochastic parabolic equations,” AIP Conference Proceedings, vol. 1389, pp. 589–592, 2011.
- A. Ashyralyev and P. E. Sobolevskii, New Difference Schemes for Partial Differential Equations, vol. 148 of Operator Theory: Advances and Applications, Birkhäuser, Berlin, Germany, 2004.
- A. A. Samarskii and E. S. Nikolaev, Nikolaev, Numerical Methods for Grid Equations, Vol. 2: Iterative Methods, Birkhäuser, Basel, Switzerland, 1989.