- 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 230190, 13 pages
On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic-Parabolic Equations
Department of Mathematics, Fatih University, 34500 Buyukcekmece, Istanbul, Turkey
Received 7 April 2012; Accepted 24 April 2012
Academic Editor: Ravshan Ashurov
Copyright © 2012 Allaberen Ashyralyev and Okan Gercek. 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.
- D. G. Gordeziani, On Methods of Resolution of a Class of Nonlocal Boundary Value Problems, Tbilisi University Press, Tbilisi, Georgia, 1981.
- A. M. Nakhushev, Equations of Mathematical Biology, Textbook for Universities, Vysshaya Shkola, Moscow, Russia, 1995.
- M. S. Salakhitdinov and A. K. Urinov, Boundary Value Problems for Equations of Mixed Type with a Spectral Parameter, Fan, Tashkent, Uzbekistan, 1997.
- A. Ashyralyev and H. A. Yurtsever, “On a nonlocal boundary value problem for semi-linear hyperbolic-parabolic equations,” Nonlinear Analysis. Theory, Methods and Applications, vol. 47, no. 5, pp. 3585–3592, 2001.
- J. I. Diaz, M. B. Lerena, J. F. Padial, and J. M. Rakotoson, “An elliptic-parabolic equation with a nonlocal term for the transient regime of a plasma in a stellarator,” Journal of Differential Equations, vol. 198, no. 2, pp. 321–355, 2004.
- D. Guidetti, B. Karasozen, and S. Piskarev, “Approximation of abstract differential equations,” Journal of Mathematical Sciences, vol. 122, no. 2, pp. 3013–3054, 2004.
- R. P. Agarwal, M. Bohner, and V. B. Shakhmurov, “Maximal regular boundary value problems in Banach-valued weighted space,” Boundary Value Problems, no. 1, pp. 9–42, 2005.
- A. Ashyralyev, G. Judakova, and P. E. Sobolevskii, “A note on the difference schemes for hyperbolic-elliptic equations,” Abstract and Applied Analysis, vol. 2006, Article ID 14816, 13 pages, 2006.
- A. S. Berdyshev and E. T. Karimov, “Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type,” Central European Journal of Mathematics, vol. 4, no. 2, pp. 183–193, 2006.
- A. Ashyralyev, C. Cuevas, and S. Piskarev, “On well-posedness of difference schemes for abstract elliptic problems in Lp([0, T]; E) spaces,” Numerical Functional Analysis and Optimization, vol. 29, no. 1-2, pp. 43–65, 2008.
- A. Ashyralyev and O. Gercek, “Nonlocal boundary value problems for elliptic-parabolic differential and difference equations,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 904824, 16 pages, 2008.
- M. De la Sen, “About the stability and positivity of a class of discrete nonlinear systems of difference equations,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 595367, 18 pages, 2008.
- P. V. Vinogradova, “Error estimates for a projection-difference method for a linear differential-operator equation,” Differential Equations, vol. 44, no. 7, pp. 970–979, 2008.
- A. Ashyralyev and Y. Ozdemir, “On stable implicit difference scheme for hyperbolic-parabolic equations in a Hilbert space,” Numerical Methods for Partial Differential Equations, vol. 25, no. 5, pp. 1100–1118, 2009.
- A. Castro, C. Cuevas, and C. Lizama, “Well-posedness of second order evolution equation on discrete time,” Journal of Difference Equations and Applications, vol. 16, no. 10, pp. 1165–1178, 2010.
- A. Ashyralyev and O. Gercek, “On second order of accuracy difference scheme of the approximate solution of nonlocal elliptic-parabolic problems,” Abstract and Applied Analysis, vol. 2010, Article ID 705172, 17 pages, 2010.
- A. Ashyralyev, “On the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 49, pp. 1–16, 2011.
- V. B. Shakhmurov, “Regular degenerate separable differential operators and applications,” Potential Analysis, vol. 35, no. 3, pp. 201–222, 2011.
- J. Martin-Vaquero, A. Queiruga-Dios, and A. H. Encinas, “Numerical algorithms for diffusion-reaction problems with non-classical conditions,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 5487–5495, 2012.
- O. Gercek, Difference Schemes of Nonlocal Boundary Value Problems for Elliptic-Parabolic Differential Equations [Ph.D. thesis], Yildiz Teknik University, Istanbul, Turkey, 2010.
- A. Ashyralyev and O. Gercek, “On multipoint nonlocal elliptic-parabolic difference problems,” Vestnik of Odessa National University, vol. 15, no. 10, pp. 135–156, 2010.
- P. E. Sobolevskii, “The coercive solvability of difference equations,” Doklady Akademii Nauk SSSR, vol. 201, pp. 1063–1066, 1971.
- A. Ashyralyev and P. E. Sobolevskii, New Difference Schemes for Partial Differential Equations, Birkhäuser, Basle, Switzerland, 2004.
- A. Ashyralyev and P. E. Sobolevskii, Well-Posedness of Parabolic Difference Equations, Birkhäuser, Basle, Switzerland, 1994.
- P. E. Sobolevskii, On Difference Methods for the Approximate Solution of Differential Equations, Voronezh State University Press, Voronezh, Russia, 1975.