TY - JOUR

T1 - Adaptive Grids and High-Order Schemes for Solving Singular Perturbation Problems

AU - Liseikin, V. D.

AU - Paasonen, V. I.

N1 - Funding Information: This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00231). Publisher Copyright: © 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/1

Y1 - 2021/1

N2 - 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.

AB - 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.

KW - boundary and interior layers

KW - grid generation method

KW - singular perturbation equations

KW - small parameter

UR - http://www.scopus.com/inward/record.url?scp=85107563073&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/e3f743ea-6d9e-3130-8a26-c88a6ddf293b/

U2 - 10.1134/S1995423921010067

DO - 10.1134/S1995423921010067

M3 - Article

AN - SCOPUS:85107563073

VL - 14

SP - 69

EP - 82

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 1

ER -