Journal of Applied Mathematics
Volume 2012 (2012), Article ID 924765, 18 pages
http://dx.doi.org/10.1155/2012/924765
Research Article

Differential Quadrature Solution of Hyperbolic Telegraph Equation

B. Pekmen1,2 and M. Tezer-Sezgin1,3

1Institute of Applied Mathematics, Middle East Technical University, 06800 Ankara, Turkey
2Department of Mathematics, Atilim University, 06836 Ankara, Turkey
3Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey

Received 10 April 2012; Accepted 15 June 2012

Academic Editor: Roberto Barrio

Copyright © 2012 B. Pekmen and M. Tezer-Sezgin. 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

Differential quadrature method (DQM) is proposed for the numerical solution of one- and two-space dimensional hyperbolic telegraph equation subject to appropriate initial and boundary conditions. Both polynomial-based differential quadrature (PDQ) and Fourier-based differential quadrature (FDQ) are used in space directions while PDQ is made use of in time direction. Numerical solution is obtained by using Gauss-Chebyshev-Lobatto grid points in space intervals and equally spaced and/or GCL grid points for the time interval. DQM in time direction gives the solution directly at a required time level or steady state without the need of iteration. DQM also has the advantage of giving quite good accuracy with considerably small number of discretization points both in space and time direction.