- 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 824819, 20 pages
Numerical Solution of Stochastic Hyperbolic Equations
1Department of Mathematics, Fatih University, 34500 Istanbul, Turkey
2Department of Applied Mathematics and Informatics, Magtymguly Turkmen State University, Ashgabat, Turkmenistan
Received 30 March 2012; Revised 25 May 2012; Accepted 27 May 2012
Academic Editor: Valery Covachev
Copyright © 2012 Necmettin Aggez and Maral Ashyralyyewa. 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 diffrential equations in a Hilbert space,” in Proceedings of the Abstracts of the National Statistics Conference, vol. 95, pp. 1–6, Ankara, Turkey, 1999.
- R. F. Curtain and P. L. Falb, “Stochastic differential equations in Hilbert space,” Journal of Differential Equations, vol. 10, pp. 412–430, 1971.
- A. Ichikawa, “Linear stochastic evolution equations in Hilbert space,” Journal of Differential Equations, vol. 28, no. 2, pp. 266–277, 1978.
- 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, Encyclopedia of Mathematics and its Applications, vol. 44, 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,” in Trudy Nauchno-Prakticheskoy Konferencii, vol. 1, pp. 85–95, Differencialniye Uravneniya i ih Prilozheniya, Ashgabat, Turkmenistan, 1993.
- P. H. Bezandry and T. Diagana, “Existence of quadratic-mean almost periodic solutions to some stochastic hyperbolic differential equations,” Electronic Journal of Differential Equations, vol. 2009, no. 111, pp. 1–14, 2009.
- 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 [Nicolson] difference schemes for stochastic parabolic equation,” Numerical Functional Analysis and Optimization. An International Journal, vol. 29, no. 3-4, pp. 268–282, 2008.
- L. Han, L. G. Han, and X. B. Gong, “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, pp. 205–244, 2009.
- A. Ashyralyev and E. M. San, “Finite difference method for stochastic parabolic equations,” in AIP Conference Proceedings, vol. 1389, pp. 589–592, 2011.
- A. Ashyralyev and M. Akat, “An approximation of stochastic hyperbolic equations,” in AIP Conference Proceedings, vol. 1389, pp. 625–628, 2011.
- S. Peszat and J. Zabczyk, “Nonlinear stochastic wave and heat equations,” Probability Theory and Related Fields, vol. 116, no. 3, pp. 421–443, 2000.
- V. Barbu, G. Da Prato, and L. Tubaro, “Stochastic wave equations with dissipative damping,” Stochastic Processes and their Applications, vol. 117, no. 8, pp. 1001–1013, 2007.
- E. Pardoux, “Stochastic partial differential equations and filtering of diffusion processes,” Stochastics, vol. 3, no. 2, pp. 127–167, 1979.
- H. O. Fattorini, Second Order Linear Differential Equations in Banach Spaces, Notas de Matematica, North-Holland Publishing, Amsterdam, The Netherlands, 1985.
- S. Piskarev and Y. Shaw, “On certain operator families related to cosine operator function,” Taiwanese Journal of Mathematics, vol. 1, no. 4, pp. 3585–3592, 1997.
- A. Ashyralyev and P. E. Sobolevskii, New Difference Schemes for Partial Differential Equations, Birkhäuser Verlag, Basel, Switzerland, 2004.
- A. Ashyralyev and H. O. Fattorini, “On uniform difference schemes for second-order singular perturbation problems in Banach spaces,” SIAM Journal on Mathematical Analysis, vol. 23, no. 1, pp. 29–54, 1992.
- P. E. Sobolevskii, Difference Methods for Approximate Solution of Differential Equations, Izdatelstvo Voronezhskogo Gosud Universiteta, Voronezh, Russia, 1975.
- A. A. Samarskii and E. S. Nikolaev, Numerical Methods for Grid Equations, vol. 2 of Iterative Methods, Birkhauser Verlag, Basel, Switzerland, 1989.