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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 1650380, 5 pages
Research Article

Unconditional Stability of a Numerical Method for the Dual-Phase-Lag Equation

Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain

Correspondence should be addressed to F. Rodríguez

Received 1 February 2017; Accepted 26 March 2017; Published 30 March 2017

Academic Editor: Filippo de Monte

Copyright © 2017 M. A. Castro 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.


The stability properties of a numerical method for the dual-phase-lag (DPL) equation are analyzed. The DPL equation has been increasingly used to model micro- and nanoscale heat conduction in engineering and bioheat transfer problems. A discretization method for the DPL equation that could yield efficient numerical solutions of 3D problems has been previously proposed, but its stability properties were only suggested by numerical experiments. In this work, the amplification matrix of the method is analyzed, and it is shown that its powers are uniformly bounded. As a result, the unconditional stability of the method is established.