174
Views
7
CrossRef citations to date
0
Altmetric
Section B

Higher-order time accurate numerical methods for singularly perturbed parabolic partial differential equations

&
Pages 1204-1214 | Received 26 Feb 2007, Accepted 01 Nov 2007, Published online: 17 Jun 2009

References

  • Chawla , M. M. and Al-Zanaidi , M. A. 1999 . An extended trapezoidal formula for diffusion equation . Comput. Math. Appl. , 38 : 51 – 59 .
  • Farrell , P. A. 2000 . Robust Computational Techniques for Boundary Layers , Boca Raton : Chapman & Hall/CRC Press .
  • Farrell , P. A. , Hemker , P. W. and Shishkin , G. I. 1996 . Discrete approximations for singularly perturbed boundary value problems with parabolic layers, I . J. Comp. Math. , 14 ( 1 ) : 71 – 97 .
  • Farrell , P. A. , Hemker , P. W. and Shishkin , G. I. 1996 . Discrete approximations for singularly perturbed boundary value problems with parabolic layers. II . J. Comp. Math. , 14 ( 2 ) : 183 – 194 .
  • Farrell , P. A. , Hemker , P. W. and Shishkin , G. I. 1996 . Discrete approximations for singularly perturbed boundary value problems with parabolic layers. III . J. Comp. Math. , 14 ( 3 ) : 273 – 290 .
  • Guo , W. and Stynes , M. 1993 . Finite element analysis of exponentially fitted lumped schemes for time-dependent convection-diffusion problems . Numer. Math. , 66 : 347 – 371 .
  • Miller , J. J.H. , O'Riordan , E. and Shishkin , G. I. 1996 . Fitted Numerical Methods for Singular Perturbation Problems , Singapore : World Scientific .
  • Miller etal , J. J.H. 1993 . Fitted mesh methods for problems with parabolic boundary layers . Math. Proc. R. Ir. Acad. , 98A ( 2 ) : 173 – 190 .
  • Natesan , S. and Deb , R. 2007 . A robust numerical scheme for singularly perturbed parabolic reaction-diffusion problems submitted for publication
  • Natesan , S. and Deb , R. 2007 . Error analysis for higher-order schemes for parabolic reaction-diffusion problems Working paper
  • Roos , H.-G. , Stynes , M. and Tobiska , L. 1996 . Numerical Methods for Singularly Perturbed Differential Equations , Berlin : Springer .
  • Stynes , M. and O'Riordan , E. 1989 . Uniformly convergent difference schemes for singularly perturbed parabolic diffusion-convection problems without turning points . Numer. Math. , 55 : 521 – 544 .

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.