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H. G. Roos, “A Note on the Conditioning of Upwind Schemes on Shishkin Meshes,” IMA Journal of Numerical Analysis, Vol. 16, No. 4, 1996, pp. 529-538. doi:10.1093/imanum/16.4.529

has been cited by the following article:

• TITLE: Analysis of an Il’in Scheme for a System of Singularly Perturbed Convection-Diffusion Equations

  AUTHORS: Mohammad Ghorbanzadeh, Asghar Kerayechian

  KEYWORDS: Convection-Diffusion, Il’in Scheme, Uniform Convergence, Singular Perturbation, Condition Number

  JOURNAL NAME: Applied Mathematics, Vol.2 No.7, July 12, 2011

  ABSTRACT: In this paper, a numerical solution for a system of singularly perturbed convection-diffusion equations is studied. The system is discretized by the Il’in scheme on a uniform mesh. It is proved that the numerical scheme has first order accuracy, which is uniform with respect to the perturbation parameters. We show that the condition number of the discrete linear system obtained from applying the Il’in scheme for a system of singularly perturbed convection-diffusion equations is O(N) and the relevant coefficient matrix is well conditioned in comparison with the matrices obtained from applying upwind finite difference schemes on this problem. Numerical results confirm the theory of the method.