Abstract
In this paper, we consider a self adjoint elliptic first boundary value problem with a small parameter affecting the highest derivative.
In the paper, we set up a new scheme by the asymptotic analysis method, compare asymptotic behavior between the solution of the difference equation and the solution of the differential equation, and show uniform convergence of the new scheme.
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Doolan, E.P., J.J.H. Miller and W.H.A. Schilders,Uniform Numerical Method for Problems with Initial and Boundary Layer (1980).
Su Yu-cheng and Wu Chi-kuang, The difference method for the solution of singular-perturbation problems for elliptic-parabolic differential equation,Applied Mathematics and Mechanics,1, 2 (1980), 175–185.
Su Yu-cheng,The Corrector Method of the Boundary Layer in the Singular Perturbation, Scientific and Technological Publishing House in Shanghai (1983). (in Chinese)
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Fa-wang, L., Xiao-su, Z. A uniformly convergent diffrence scheme for the singular perturbation of a self adjoint elliptic partial differential equation. Appl Math Mech 7, 495–504 (1986). https://doi.org/10.1007/BF01895769
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DOI: https://doi.org/10.1007/BF01895769