Abstract
The error generated by the classical upwind finite difference method on a uniform mesh, when applied to a class of singularly perturbed modelordinary different alequations with a singularly perturbed Neumann boundary condition, tends to infinity as the singular perturbation parameter tends to zero. Note that the exact solution is uniformly bounded with respect to the perturbat on parameter. For the same classcal finite difference operator on an appropriate piecewise -uniform mesh, it is shown that the numerical solutions converge, uniformly with respect to the perturbation parameter, to the exact solution of any problem from this class.
This research was supported in part by the Russian Foundation for Basic Research under grant No.98-01-00362, by the National Science Foundation grant DMS- 9627244 and by the Enterprise Ireland grant SC-98-612.
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References
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© 2001 Springer-Verlag Berlin Heidelberg
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Farrell, P.A., Hegart, A.F., Miller, J.J.H., O’Riordan, E., Shishkin, G.I. (2001). Parameter-Uniform Numerical Methods for a Class of Singularly Perturbed Problems with a Neumann Boundary Condition. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_35
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DOI: https://doi.org/10.1007/3-540-45262-1_35
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