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The Scientific World Journal
Volume 2014, Article ID 497393, 7 pages
http://dx.doi.org/10.1155/2014/497393
Research Article

Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations

1Department of Mathematics, Faculty of Art and Science, Sinop University, 57000 Sinop, Turkey
2Department of Mathematics, Faculty of Science, Yüzüncü Yil University, 65080 Van, Turkey
3Department of Mathematics, Faculty of Education, Yüzüncü Yil University, 65080 Van, Turkey

Received 21 August 2013; Accepted 2 December 2013; Published 4 February 2014

Academic Editors: C.-s. Liu and N. I. Mahmudov

Copyright © 2014 I. Amirali et al. 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.

Abstract

Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown.