Numerical approximations to the scaled first derivatives of a two parameter singularly perturbed problem

2017/08/02 by O'Riordan, Eugene, Pickett, Maria
#65L11 #65L12 #65L70 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1708.00682

Abstract

A singularly perturbed problem involving two singular perturbation parameters is discretized using the classical upwinded finite difference scheme on an appropriate piecewise-uniform Shishkin mesh. Scaled discrete derivatives (with scaling only used within the layers) are shown to be parameter uniformly convergent to the scaled first derivatives of the continuous solution.

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