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A.S. Bakhvalov, On the optimization of methods for solving boundary value problems in the presence of boundary layers, Zh. Vychisl. Mat. Mat. Fiz. 9(1969) 841-859 (in Russian).

has been cited by the following article:

• TITLE: The uniform convergence of upwind schemes on layer-adapted meshes for a singularly perturbed Robin BVP

  AUTHORS: Quan Zheng, Fengxi Huang, Xiaoli Feng, Mengbin Han

  KEYWORDS: Singularly perturbed Robin BVP; simple upwind scheme; midpoint upwind scheme; layer-adapted mesh; uniform convergence

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.2 No.4B, January 11, 2013

  ABSTRACT: In this paper, we discuss the uniform convergence of the simple upwind scheme on the Shishkin mesh and the Bakhvalov-Shishkin mesh for solving a singularly perturbed Robin boundary value problem, and investigate the midpoint upwind scheme on the Shishkin mesh and the Bakhvalov-Shishkin mesh to achieve better uniform convergence. The elaborate ε-uniform pointwise estimates are proved by using the comparison principle and barrier functions. The numerical experiments support the theoretical results for the schemes on the meshes.