- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 454831, 22 pages
FDM for Elliptic Equations with Bitsadze-Samarskii-Dirichlet Conditions
1Department of Mathematics, Fatih University, 34500 Istanbul, Turkey
2Department of Mathematics, ITTU, 74400 Ashgabat, Turkmenistan
Received 8 April 2012; Accepted 6 May 2012
Academic Editor: Ravshan Ashurov
Copyright © 2012 Allaberen Ashyralyev and Fatma Songul Ozesenli Tetikoglu. 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.
- O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Equations of Elliptic Type, Nauka, Moscow, Russia, 1973.
- M. L. Vishik, A. D. Myshkis, and O. A. Oleinik, “Partial differential equations,” in Mathematics in USSR in the Last 40 Years, 1917–1957, vol. 1, pp. 563–599, Fizmatgiz, Moscow, Russia, 1959.
- S. G. Krein, Linear Differential Equations in Banach Space, Nauka, Moscow, Russia, 1966.
- V. L. Gorbachuk and M. L. Gorbachuk, Boundary Value Problems for Differential-Operator Equations, Naukova Dumka, Kiev, Russia, 1984.
- G. Berikelashvili, “On a nonlocal boundary-value problem for two-dimensional elliptic equation,” Computational Methods in Applied Mathematics, vol. 3, no. 1, pp. 35–44, 2003.
- F. Criado-Aldeanueva, F. Criado, N. Odishelidze, and J. M. Sanchez, “On a control problem governed by a linear partial differential equation with a smooth functional,” Optimal Control Applications & Methods, vol. 31, no. 6, pp. 497–503, 2010.
- A. Ashyralyev, “Nonlocal boundary-value problems for elliptic equations: well-posedness in Bochner spaces,” in Proceedings of the ICMS International Conference on Mathematical Science, vol. 1309 of AIP Conference Proceedings, pp. 66–84, Bolu, Turkey, November 2010.
- A. Ashyralyev, “On well-posedness of the nonlocal boundary value problems for elliptic equations,” Numerical Functional Analysis and Optimization, vol. 24, no. 1-2, pp. 1–15, 2003.
- I. A. Gurbanov and A. A. Dosiev, “On the numerical solution of nonlocal boundary problems for quasilinear elliptic equations,” in Approximate Methods for Operator Equations, pp. 64–74, Baku State University, Baku, Azerbaijan, 1984.
- A. A. Samarskii and E. S. Nikolaev, Numerical Methods for Grid Equations, 2 Iterative Methods, Birkhäuser, Basel, Switzerland, 1989.
- A. Ashyralyev, C. Cuevas, and S. Piskarev, “On well-posedness of difference schemes for abstract elliptic problems in spaces,” Numerical Functional Analysis and Optimization, vol. 29, no. 1-2, pp. 43–65, 2008.
- A. V. Bitsadze and A. A. Samarskii, “On some simplest generalizations of linear elliptic problems,” Doklady Akademii Nauk SSSR, vol. 185, pp. 739–740, 1969.
- A. Ashyralyev and E. Ozturk, “Numerical solutions of Bitsadze-Samarskii problem for elliptic equations,” in Further Progress in Analysis: Proceedings of the 6th International ISAAC Congress Ankara, Turkey 13–18 August 2007, pp. 698–707, World Scientific, 2009.
- A. P. Soldatov, “A problem of Bitsadze-Samarskii type for second-order elliptic systems on the plane,” Russian in Doklady Akademii Nauk, vol. 410, no. 5, pp. 607–611, 2006.
- D. G. Gordeziani, “On a method of resolution of Bitsadze-Samarskii boundary value problem,” Abstracts of Reports of Institute of Applied Mathematics, vol. 2, pp. 38––40, 1970.
- D. V. Kapanadze, “On the Bitsadze-Samarskii nonlocal boundary value problem,” Differential Equations, vol. 23, no. 3, pp. 543–545, 1987.
- A. Ashyralyev, “A note on the Bitsadze-Samarskii type nonlocal boundary value problem in a Banach space,” Journal of Mathematical Analysis and Applications, vol. 344, no. 1, pp. 557–573, 2008.
- R. P. Agarwal and V. B. Shakhmurov, “Multipoint problems for degenerate abstract differential equations,” Acta Mathematica Hungarica, vol. 123, no. 1-2, pp. 65–89, 2009.
- V. Shakhmurov and R. Shahmurov, “Maximal B-regular integro-differential equation,” Chinese Annals of Mathematics B, vol. 30, no. 1, pp. 39–50, 2009.
- D. Orlovsky and S. Piskarev, “On approximation of inverse problems for abstract elliptic problems,” Journal of Inverse and Ill-Posed Problems, vol. 17, no. 8, pp. 765–782, 2009.
- P. E. Sobolevskii, Difference Methods for the Approximate Solution of Differential Equations, Voronezh State University, Voronezh, Russia, 1975.