88
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

A fitted mesh method for a coupled semi-linear system of singularly perturbed initial value problems

&

References

  • G. Steven and H. R. Krantz, Parks: The Implicit Function Theorem History, Theory and Applications. Berlin: Springer Science + Business Media, LLC, 2003.
  • K. W. Chang and F. A. Howes, Nonlinear Singular Perturbation Phenomena: Theory and Application, Applied Mathematical Sciences. New York: Springer Science + Business Media New York Inc, 1984.
  • R. E. O’Malley, “On nonlinear singularly perturbed initial value problems,” SIAM Rev., vol. 30, no. 2, pp. 193–212, 1988.
  • P. V. Kokotovi, “Applications of singular perturbation techniques to control problems,” SIAM Rev., vol. 26, no. 4, pp. 501–550, 1984.
  • R. Vulanovic, P. A. Farrell and P. Lin, “Numerical solution of non-linear singular perturbation problems modeling chemical reactions,” Applications of Advanced Computational Methods for Boundary and Interior Layers, J. J. H. Miller, Ed., Dublin, Ireland: Boole Press, 1993, pp. 192–213.
  • E. P. Doolan, J. J. H. Miller and W. H. A. Schilders, Uniform Numerical Methods for Problems with Initial and Boundary Layers. Dublin, Ireland: Boole Press, 1980.
  • P. A. Farrell, A. Hegarty, J. J. H. Miller, E. O’Riordan and G. I. Shishkin, Robust Computational Techniques for Boundary Layers. Boca Raton, FL: Chapman and Hall/CRC Press, 2000.
  • P. A. Farrell, J. J. H. Miller, E. O’Riordan and G. I. Shishkin, “A uniformly convergent finite difference scheme for a singularly perturbed semilinear equation,” SIAM J. Numer. Anal., vol. 33, no. 3, pp. 1135–1149, 1996. DOI: 10.1137/0733056.
  • J. J. H. Miller, E. O’Riordan and G. I. Shishkin, Fitted Numerical Methods for Singular Perturbation Problems. Singapore: World Scientific Publishing Co., 1996.
  • S. Valarmathi and J. J. H. Miller, “A parameter-uniform finite difference method for singularly perturbed linear dynamical systems,” Int. J. Numer. Anal. Model., vol. 7, no. 3, pp. 535–548, 2010.
  • J. L. Gracia, F. J. Lisbona, M. Madaune-Tort, E. O’Riordan, et al., “A system of singularly perturbed semilinear equations,” in BAIL 2008 – Boundary and Interior Layers. Lecture Notes in Computational Science and Engineering, A. F. Hegarty, Eds. Berlin Heidelberg: Springer-Verlag, 2009.
  • N. Shivaranjani, J. J. H. Miller and S. Valarmathi, “A parameter uniform almost first order convergent numerical method for a semi-linear system of singularly perturbed delay differential equations,” Biomath, vol. 3, 1411041 (pp. 1–8), 2014.
  • M. Manikandan and A. Tamilselvan, “An efficient numericalmethod for a nonlinear system of singularly perturbed differential equations arising in a two-time scale system,” J. Appl. Math. Comput. vol. 68, no. 3, pp.1069-1086, 2022 DOI: 10.1007/s12190-021-01559-0.
  • Z. Cen, A. Xu and A. Le, “A second-order hybrid finite difference scheme for a system of singularly perturbed initial value problems,” J. Comput. Appl. Math., vol. 234, no. 12, pp. 3445–3457, 2010. DOI: 10.1016/j.cam.2010.05.006.

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.