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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 686483, 10 pages
http://dx.doi.org/10.1155/2013/686483
Research Article

Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, 34210 Istanbul, Turkey

Received 4 March 2013; Accepted 12 June 2013

Academic Editor: Adem Kılıçman

Copyright © 2013 Aydin Secer. 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. F. Stenger, “A Sinc-Galerkin method of solution of boundary value problems,” Mathematics of Computation, vol. 33, no. 145, pp. 85–109, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. F. Stenger, “Summary of Sinc numerical methods,” Journal of Computational and Applied Mathematics, vol. 121, no. 1-2, pp. 379–420, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. F. Stenger, “Approximations via Whittaker's cardinal function,” Journal of Approximation Theory, vol. 17, no. 3, pp. 222–240, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. E. T. Whittaker, “On the functions which are represented by the expansions of the interpolation theory,” Proceedings of the Royal Society of Edinburg, vol. 35, pp. 181–194, 1915.
  5. J. M. Whittaker, Interpolation Function Theory, Cambridge Tracts in Mathematics and Mathematical Physics, no. 33, Cambridge University Press, London, UK, 1935, by E. F. Beckenbach, McGraw-Hill, New York, NY, USA, 1961.
  6. J. Lund, “Symmetrization of the sinc-Galerkin method for boundary value problems,” Mathematics of Computation, vol. 47, no. 176, pp. 571–588, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. Secer and M. Kurulay, “The Sinc-Galerkin method and its applications on singular Dirichlet-type boundary value problems,” Boundary Value Problems, vol. 2012, article 126, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  8. K. M. McArthur, K. L. Bowers, and J. Lund, “Numerical implementation of the Sinc-Galerkin method for second-order hyperbolic equations,” Numerical Methods for Partial Differential Equations, vol. 3, no. 3, pp. 169–185, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. Saadatmandi, M. Razzaghi, and M. Dehghan, “Sinc-Galerkin solution for nonlinear two-point boundary value problems with applications to chemical reactor theory,” Mathematical and Computer Modelling, vol. 42, no. 11-12, pp. 1237–1244, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. A. Secer, M. Kurulay, M. Bayram, and M. A. Akinlar, “An efficient computer application of the Sinc-Galerkin approximation for nonlinear boundary value problems,” Boundary Value Problems, vol. 2012, article 117, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  11. J. Rashidinia, K. Maleknejad, and N. Taheri, “Sinc-Galerkin method for numerical solution of the Bratu's problems,” Numerical Algorithms, vol. 62, no. 1, pp. 1–11, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. A. Shidfar and A. Babaei, “The sinc-Galerkin method for solving an inverse parabolic problem with unknown source term,” Numerical Methods for Partial Differential Equations, vol. 29, no. 1, pp. 64–78, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. M. Zarebnia and M. G. A. Abadi, “A numerical sinc method for systems of integro-differential equations,” Physica Scripta, vol. 82, no. 5, Article ID 055011, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. J. Lund and K. L. Bowers, Sinc Methods for Quadrature and Differential Equations, SIAM, Philadelphia, Pa, USA, 1992. View at Publisher · View at Google Scholar · View at MathSciNet