论文信息 - A second order accurate, positive scheme for singularly perturbed boundary value problems

A second order accurate, positive scheme for singularly perturbed boundary value problems

AbstractWe give a novel finite difference method for singularly perturbed boundary value problems in $$\mathbb{R}^{\text{1}}$$ . The method is of positive type in 1−D with errors of O(h2 + εh) in regions a few meshpoints away from possible layers, where ε is the small parameter in the differential equation. Global and local error estimates are proven for the method and numerical experiments are presented. Possible extension to 2−D as a monotone scheme is considered, but more questons are unsolved than solved in 2−D.

William Layton | Vincent J. Ervin | W. Layton | V. Ervin

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