Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations

Amirali I., Amiraliyev G. M., Çakır M., Çimen E.

SCIENTIFIC WORLD JOURNAL, 2014 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2014
  • Doi Number: 10.1155/2014/497393
  • Journal Name: SCIENTIFIC WORLD JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Van Yüzüncü Yıl University Affiliated: Yes

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.