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- W2349042912 abstract "Aimed at singularly perturbed elliptic partial differential equation with periodical boundary value problem,an effective numerical method was constructed.Adaptive convergence was proved.Effective computational result was obtained with few number grid when the parameter was small.Firstly,the property of boundary layer was discussed.The solution was decomposed into the smooth component and the singular component.The derivatives of the smooth component and the singular component were estimated.Secondly,finite difference method was proposed on the Shishkin mesh.The discrete maximum principle and the uniform stability result were studied.Thirdly,uniform convergence is proved by constructing the barrier function.Finally,numerical experiment was proposed to support the theoretical result.Numerical results show that the presented method fitted the property of boundary layer well.The solution for this kind of multi-scale problem was provided in theory.The presented numerical method can be applied to calculate other singularly perturbed problems." @default.
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- W2349042912 date "2010-12-23" @default.
- W2349042912 modified "2023-09-25" @default.
- W2349042912 title "Adaptive numerical method for singularly perturbed equation with periodical boundary value problem" @default.
- W2349042912 doi "https://doi.org/10.3785/j.issn.1008973x.2010.11.031" @default.
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