331
Views
27
CrossRef citations to date
0
Altmetric
Original Articles

Second-order uniformly convergent numerical method for singularly perturbed delay parabolic partial differential equations

& ORCID Icon
Pages 490-510 | Received 26 Feb 2016, Accepted 08 Sep 2016, Published online: 28 Feb 2017

References

  • A.R. Ansari, S.A. Bakr, and G.I. Shishkin, A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations, J. Comput. Appl. Math. 205 (2007), pp. 552–566. doi: 10.1016/j.cam.2006.05.032
  • A. Das and S. Natesan, Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection-diffusion problems on Shishkin mesh, Appl. Math. Comput. 271 (2015), pp. 168–186.
  • B.S. Deb and S. Natesan, Richardson extrapolation method for singularly perturbed coupled system of convection-diffusion boundary-value problems, CMES Comput. Model. Eng. Sci. 38 (2008), pp. 179–200.
  • S. Gowrisankar and S. Natesan, A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problems on equidistributed grids, Electron. Trans. Numer. Anal. 41 (2014), pp. 376–395.
  • S. Gowrisankar and S. Natesan, ε-Uniformly convergent numerical scheme for singularly perturbed delay parabolic partial differential equations, Int. J. Comput. Math. (2016), doi:doi: 10.1080/00207160.2016.1154948.
  • H.B. Keller, Numerical Methods for Two-Point boundary Value Problems, Dover, New York, 1992.
  • J. Mohapatra and S. Natesan, Uniformly convergent second-order numerical method for singularly perturbed delay differential equations, Neural Parallel Sci. Comput. 16 (2008), pp. 353–370.
  • K. Mukherjee and S. Natesan, Richardson extrapolation technique for singularly perturbed parabolic convection-diffusion problems, Computing 92 (2011), pp. 1–32. doi: 10.1007/s00607-010-0126-8
  • M.C. Natividad and M. Stynes, Richardson extrapolation for a convection-diffusion problem using a Shishkin mesh, Appl. Numer. Math. 45 (2003), pp. 315–329. doi: 10.1016/S0168-9274(02)00212-X
  • M. Stynes and H.G. Roos, The midpoint upwind scheme, Appl. Numer. Math. 23 (1997), pp. 361–374. doi: 10.1016/S0168-9274(96)00071-2
  • P.K.C. Wang, Asymptotic stability of a time-delayed diffusion system, J. Appl. Mech. 30 (1963), pp. 500–504. doi: 10.1115/1.3636609

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.