Table of Contents Author Guidelines Submit a Manuscript
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.

Linked References

  1. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford University Press, New York, NY, USA, 2nd edition, 1959.
  2. J. Zierep and C. Fetecau, “Energetic balance for the rayleigh-stokes problem of a maxwell fluid,” International Journal of Engineering Science, vol. 45, no. 2-8, pp. 617–627, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  3. H. Pascal, “Pressure wave propagation in a fluid flowing through a porous medium and problems related to interpretation of Stoneley's wave attenuation in acoustical well logging,” International Journal of Engineering Science, vol. 24, no. 9, pp. 1553–1570, 1986. View at Publisher · View at Google Scholar · View at Scopus
  4. M. E. Davis and L. L. Vanzandt, “Microwave response of DNA in solution: theory,” Physical Review A: Atomic, Molecular and Optical Physics, vol. 37, no. 3, pp. 888–901, 1988. View at Publisher · View at Google Scholar · View at Scopus
  5. R. Ortega and A. M. Robles-Perez, “A maximum principle for periodic solutions of the telegraph equation,” Journal of Mathematical Analysis and Applications, vol. 221, no. 2, pp. 625–651, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J. Mawhin, R. Ortega, and A. M. Robles-Perez, “A maximum principle for bounded solutions of the telegraph equations and applications to nonlinear forcings,” Journal of Mathematical Analysis and Applications, vol. 251, no. 2, pp. 695–709, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  7. Y. Li, “Maximum principles and the method of upper and lower solutions for time-periodic problems of the telegraph equations,” Journal of Mathematical Analysis and Applications, vol. 327, no. 2, pp. 997–1009, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. F. Wang and Y. An, “A generalized quasilinearization method for telegraph system,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 407–413, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. R. Bellman and R. Kalaba, Quasilinearization and Nonlinear Boundary Value Problems, Elsevier, New York, NY, USA, 1965.
  10. V. Lakshmikantham and A. S. Vatsala, Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishers, Dodrecht, The Netherlands, 1998.
  11. R. N. Mohapatra, K. Vajravelu, and Y. Yin, “Generalized quasilinearization method and rapid convergence for first order initial value problems,” Journal of Mathematical Analysis and Applications, vol. 207, no. 1, pp. 206–219, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. A. Cabada, J. J. Nieto, and S. Heikkila, “Rapid convergence of approximate solutions for first order nonlinear boundary value problems,” International Journal of Mathematics and Mathematical Sciences, vol. 21, no. 3, pp. 499–505, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  13. T. G. Melton and A. S. Vatsala, “Generalized quasilinearization method and higher order of convergence for second-order boundary value problems,” Boundary Value Problems, vol. 2006, Article ID 25715, 15 pages, 2006. View at Publisher · View at Google Scholar · View at Scopus
  14. T. G. Melton and A. S. Vatsala, “Higher order convergence via generalized quasilinearization method for impulsive differential equations,” in Proceedings of the 1st International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS-09, vol. 1186, pp. 284–291, June 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. T. G. Melton and A. S. Vatsala, “Improved generalized quasilinearization method and rapid convergence for reaction diffusion equations,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 563–572, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. T. G. Melton and A. S. Vatsala, “Higher order of convergence via generalized quasilinearization method for parabolic integro-differential equations,” Communications in Applied Analysis. An International Journal for Theory and Applications, vol. 11, no. 3-4, pp. 403–418, 2007. View at Google Scholar · View at MathSciNet
  17. S. S. Motsa and P. Sibanda, “Some modifications of the quasilinearization method with higher-order convergence for solving nonlinear BVPs,” Numerical Algorithms, vol. 63, no. 3, pp. 399–417, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  18. P. Wang and X. Liu, “Rapid convergence of approximate solutions for singular differential systems,” Electronic Journal of Differential Equations, vol. 2015, no. 203, pp. 1–12, 2015. View at Google Scholar