Adaptive Grids and High-Order Schemes for Solving Singular Perturbation Problems

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

Layer-resolving grids remain important elements of software codes for solving real problems in layers with singularities, since they can substantially enhance the efficiency of computer resources. This paper describes an explicit approach to generating layer-resolving grids, which is aimed at using difference schemes of arbitrary orders. The approach is based on estimates of derivatives of solutions to singular perturbation problems; it is a generalization of an approach that has been developed for first-order schemes. The layer-resolving grids proposed are suitable to tackle problems with exponential-, power-, logarithmic-, and mixed-type boundary and interior layers. The theoretical results are confirmed by numerical experiments on a number of test problems with such layers performed with difference schemes of various orders of accuracy.

Язык оригиналаанглийский
Страницы (с-по)69-82
Число страниц14
ЖурналNumerical Analysis and Applications
Том14
Номер выпуска1
DOI
СостояниеОпубликовано - янв 2021

Предметные области OECD FOS+WOS

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