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Abstract
A singularly perturbed transport equation is considered. A variable two-step backward differentiation formulas (BDF2) on a Shishkin-type mesh is used to discrete the first-order derivatives of the singularly perturbed transport equation. The stability and error analysis are derived by using the discrete orthogonal convolution kernels. It is proved that the scheme is second-order uniformly convergent with respect to the small parameter, which improves previous results. Numerical experiments are presented to support the theoretical result.
Acknowledgements
We would like to thank the anonymous reviewers for some suggestions for the improvement of this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
The work was supported by Ningbo Municipal Natural Science Foundation (Grant No. 2023J203), Zhejiang Provincial Natural Science Foundation of China (Grant No. LTGY23H240002) and Zhejiang Province Higher Education Teaching Reform Project (Grant No. jg20220457).