About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 840621, 14 pages
http://dx.doi.org/10.1155/2012/840621
Research Article

An Approximation of Ultra-Parabolic Equations

1Department of Mathematics, Fatih University, Istanbul, Turkey
2Department of Mathematics, ITTU, Ashgabat, Turkmenistan, Turkey

Received 7 February 2012; Accepted 3 April 2012

Academic Editor: Hasan Ali Yurtsever

Copyright © 2012 Allaberen Ashyralyev and Serhat Yılmaz. 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.

Linked References

  1. J. Dyson, E. Sanchez, R. Villella-Bressan, and G. F. Webb, “An age and spatially structured model of tumor invasion with haptotaxis,” Discrete and Continuous Dynamical Systems B, vol. 8, no. 1, pp. 45–60, 2007. View at Publisher · View at Google Scholar
  2. K. Kunisch, W. Schappacher, and G. F. Webb, “Nonlinear age-dependent population dynamics with random diffusion,” Computers & Mathematics with Applications, vol. 11, no. 1–3, pp. 155–173, 1985, Hyperbolic partial differential equations, II. View at Publisher · View at Google Scholar
  3. A. N. Kolmogorov, “Zur Theorie der stetigen zufälligen Prozesse,” Mathematische Annalen, vol. 108, pp. 149–160, 1933.
  4. A. N. Kolmogorov, “Zufällige Bewegungen,” Annals of Mathematics, vol. 35, pp. 116–117, 1934.
  5. T. G. Genčev, “On ultraparabolic equations,” Doklady Akademii Nauk SSSR, vol. 151, pp. 265–268, 1963.
  6. Q. Deng and T. G. Hallam, “An age structured population model in a spatially heterogeneous environment: existence and uniqueness theory,” Nonlinear Analysis, vol. 65, no. 2, pp. 379–394, 2006. View at Publisher · View at Google Scholar
  7. G. di Blasio and L. Lamberti, “An initial-boundary value problem for age-dependent population diffusion,” SIAM Journal on Applied Mathematics, vol. 35, no. 3, pp. 593–615, 1978. View at Publisher · View at Google Scholar
  8. G. di Blasio, “Nonlinear age-dependent population diffusion,” Journal of Mathematical Biology, vol. 8, no. 3, pp. 265–284, 1979. View at Publisher · View at Google Scholar
  9. S. A. Tersenov, “Boundary value problems for a class of ultraparabolic equations and their applications,” Matematicheskiĭ Sbornik, vol. 133(175), no. 4, pp. 529–544, 1987.
  10. G. Akrivis, M. Crouzeix, and V. Thomée, “Numerical methods for ultraparabolic equations,” Calcolo, vol. 31, no. 3-4, pp. 179–190, 1994. View at Publisher · View at Google Scholar
  11. A. Ashyralyev and S. Yılmaz, “On the approximate solution of ultra parabolic equations,” in Proceedings of the 2nd International Symposium on Computing in Science & Engineering, M. Güneş, A. K. Çınar, and I. Gürler, Eds., pp. 533––535, Gediz University, Izmir, Turkey, 2011.
  12. A. Ashyralyev and S. Yılmaz, “Second order of accuracy difference schemes for ultra parabolic equations,” AIP Conference Proceedings, vol. 1389, pp. 601–604, 2011. View at Publisher · View at Google Scholar
  13. A. Ashyralyev and P. E. Sobolevskii, Well-Posedness of Parabolic Difference Equations Operator Theory Advance and Applications, vol. 69, Birkh äuser, Basel, Switzerland, 1994.
  14. P. E. Sobolevskii, “On the Crank-Nicolson difference scheme for parabolic equations,” Nonlinear Oscillations and Control Theory, pp. 98–106, 1978.
  15. A. A. Samarskii and E. S. Nikolaev, Numerical Methods for Grid Equations. Vol. 2: Iterative Methods, Birkhäuser, Basel, Switzerland, 1989.