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Discrete Dynamics in Nature and Society
Volume 2011, Article ID 561015, 17 pages
Research Article

An Operator-Difference Method for Telegraph Equations Arising in Transmission Lines

Department of Elementary Mathematics Education, Mevlana University, 42003 Konya, Turkey

Received 12 June 2011; Accepted 3 August 2011

Academic Editor: Hassan A. El-Morshedy

Copyright © 2011 Mehmet Emir Koksal. 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.


A second-order linear hyperbolic equation with time-derivative term subject to appropriate initial and Dirichlet boundary conditions is considered. Second-order unconditionally absolutely stable difference scheme in (Ashyralyev et al. 2011) generated by integer powers of space operator is modified for the equation. This difference scheme is unconditionally absolutely stable. Stability estimates for the solution of the difference scheme are presented. Various numerical examples are tested for showing the usefulness of the difference scheme. Numerical solutions of the examples are provided using modified unconditionally absolutely stable second-order operator-difference scheme. Finally, the obtained results are discussed by comparing with other existing numerical solutions. The modified difference scheme is applied to analyze a real engineering problem related with a lossy power transmission line.