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Mathematics of Computation

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An analysis of a superconvergence result for a singularly perturbed boundary value problem

Authors: Eugene O’Riordan and Martin Stynes
Journal: Math. Comp. 46 (1986), 81-92
MSC: Primary 65L10
MathSciNet review: 815833
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Abstract: We give a new proof that the El-Mistikawy and Werle finite-difference scheme is uniformly second-order accurate for a nonselfadjoint singularly perturbed boundary value problem. To do this, we use exponential finite elements and a discretized Green’s function. The proof is direct, gives the nodal errors explicitly in integral form, and involves much less computation than in previous proofs of the result.

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Article copyright: © Copyright 1986 American Mathematical Society