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.