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

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Abstract

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.

Original languageEnglish
Pages (from-to)69-82
Number of pages14
JournalNumerical Analysis and Applications
Volume14
Issue number1
DOIs
Publication statusPublished - Jan 2021

Keywords

  • boundary and interior layers
  • grid generation method
  • singular perturbation equations
  • small parameter

OECD FOS+WOS

  • 1.01 MATHEMATICS

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