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Journal of Function Spaces
Volume 2017, Article ID 1982568, 10 pages
https://doi.org/10.1155/2017/1982568
Research Article

Rapid Convergence for Telegraph Systems with Periodic Boundary Conditions

1College of Electronic and Information Engineering, Hebei University, Baoding 071002, China
2College of Mathematics and Information Science, Hebei University, Baoding 071002, China

Correspondence should be addressed to Peiguang Wang; nc.ude.ubh@gnawgp

Received 4 July 2017; Revised 7 October 2017; Accepted 19 October 2017; Published 13 November 2017

Academic Editor: Xinguang Zhang

Copyright © 2017 Peiguang Wang and Xiang Liu. 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 generalized quasilinearization method is applied in this paper to a telegraph system with periodic boundary conditions. We consider the case in which the forcing function satisfies the following condition: exists and is quasimonotone nondecreasing or nonincreasing. We develop nonlinear iterates of order which will be different with being even or odd. Finally, we develop two sequences which converge to the solution of the telegraph system and the convergence is of order .