Abstract
We consider a singularly perturbed initial-third boundary value Sobolev problem. Firstly, the asymptotic behaviour of the exact solution is analysed. Then, a second-order finite difference scheme is constructed on the special non-uniform mesh. By using energy estimate, the stability and convergence of the proposed scheme are investigated in the discrete energy norm. Finally, three numerical examples are solved to validate the theory.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Correction Statement
This article was originally published with errors, which have now been corrected in the online version. Please see Correction (http://dx.doi.org/10.1080/10236198.2023.2254625)