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Advances in Mathematical Physics
Volume 2016 (2016), Article ID 7045657, 10 pages
http://dx.doi.org/10.1155/2016/7045657
Research Article

A New Unconditionally Stable Method for Telegraph Equation Based on Associated Hermite Orthogonal Functions

College of Defense Engineering, PLA University of Science and Technology, Nanjing 210007, China

Received 22 September 2016; Accepted 4 December 2016

Academic Editor: Stephen C. Anco

Copyright © 2016 Di Zhang 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

The present paper proposes a new unconditionally stable method to solve telegraph equation by using associated Hermite (AH) orthogonal functions. Unlike other numerical approaches, the time variables in the given equation can be handled analytically by AH basis functions. By using the Galerkin’s method, one can eliminate the time variables from calculations, which results in a series of implicit equations. And the coefficients of results for all orders can then be obtained by the expanded equations and the numerical results can be reconstructed during the computing process. The precision and stability of the proposed method are proved by some examples, which show the numerical solution acquired is acceptable when compared with some existing methods.