45
Views
0
CrossRef citations to date
0
Altmetric
Research Article

A BDF2 method for a singularly perturbed transport equation

&
Pages 538-548 | Received 10 Mar 2023, Accepted 29 Apr 2024, Published online: 09 May 2024

References

  • J.L. Gracia, A. Navas-Montilla, and E. O'Riordan, Parameter-uniform numerical methods for singularly perturbed linear transport problems. Math. Meth. Appl. Sci. 45 (2022), pp. 11224–11245.
  • H.L. Liao, B. Ji, and L. Zhang, An adaptive BDF2 implicit time-stepping method for the phase field crystal model. IMA J. Numer. Anal. 42(1) (2022), pp. 649–679.
  • H.L. Liao, and Z. Zhang, Analysis of adaptive BDF2 scheme for diffusion equations. Math. Comput. 90(329) (2021), pp. 1207–1226.
  • L.-B. Liu, Y. Liao, and G. Long, A novel parameter-uniform numerical method for a singularly perturbed volterra integro-differential equation. Comp. Appl. Math. 42(1) (2023), pp. 12.
  • X. Meng, and M. Stynes, Balanced and energy norm error bounds for a spatial FEM with Crank-Nicolson and BDF2 time discretization applied to a singularly perturbed reaction-diffusion problem. Numer. Algor. 95(3) (2024), pp. 1155–1176.
  • G.I. Shishkin, Difference scheme for an initial-boundary value problem for a singularly perturbed transport equation. Comput. Math. Math. Phys. 57(11) (2017), pp. 1789–1795.
  • G.I. Shishkin, and L.P. Shishkina, A difference scheme of the decomposition method for an initial boundary value problem for the singularly perturbed transport equation. Comput. Math. Math. Phys. 62(7) (2022), pp. 1193–1201.
  • L. Shishkina, and G.I. Shishkin, Development and numerical study of robust difference schemes for a singularly perturbed transport equation, in Finite Difference Methods: Theory and Applications, FDM 2018, Lecture Notes in Computational Science and Engineering, I. Dimov, I. Farago, L. Vulkov, eds., Springer, Cham, Switzerland, 2019. pp. 476–483.
  • J.J.H. Miller, E. O’Riordan, and G.I. Shishkin, Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in one and two Dimensions, revised ed., World Scientific Publishing Co., NJ, USA, 2012.
  • D. Willett, and J.S.W. Wong, On the discrete analogues of some generalizations of Gronwall's inequality. Monatsh. Math. 69(4) (1965), pp. 362–367.

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.