Abstract
In this paper, we consider the upwind difference scheme for singular perturbation problem (1.1). On a special discretization mesh, it is proved that the solution of the upwind difference scheme is first order convergent, uniformly in the small parameter ε, to the solution of problem (1.1). Numerical results are finally provided.
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References
Wang Guo-ying, The difference method for solving singular perturbation problems of the second order elliptic partial differential equations,Numerical Mathematics, A Journal of Chinese Universities,7, 2 (1985), 151–160. (in Chinese)
Wang Guo-ying, A class of uniformly convergent difference scheme for the second order elliptic partial differential equations,Mathematical Biquarterly, Journal of Nanjing University,2, 1 (1988). 102–106. (in Chinese)
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Qi-guang, W., Xiao-di, S. Numerical solution of a singularly perturbed elliptichyperbolic partial differential equation on a nonuniform discretization mesh. Appl Math Mech 13, 1081–1088 (1992). https://doi.org/10.1007/BF02456147
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DOI: https://doi.org/10.1007/BF02456147