Investigation of a Two-Grid Method of Improved Accuracy for the Elliptic Reaction–Diffusion Equation with Boundary Layers
A two-grid method for the elliptic equation with a small parameter ε multiplying the highest derivative is investigated. The ε-uniformly convergent difference scheme on the Shishkin mesh is considered. To resolve the difference scheme, a two-grid method with ε-uniform interpolation formula is used....
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| Language: | English |
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Kazan Federal University
2015-03-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://kpfu.ru/portal/docs/F_887599187/157_1_phys_mat_7.pdf |
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| author | S.V. Tikhovskaya |
| author_facet | S.V. Tikhovskaya |
| author_sort | S.V. Tikhovskaya |
| collection | DOAJ |
| description | A two-grid method for the elliptic equation with a small parameter ε multiplying the highest derivative is investigated. The ε-uniformly convergent difference scheme on the Shishkin mesh is considered. To resolve the difference scheme, a two-grid method with ε-uniform interpolation formula is used. To increase the accuracy of the scheme, the Richardson extrapolation in the two-grid method is applied. The results of numerical experiments are discussed. Various iterative methods for implementation of the two-grid algorithm are suggested. |
| format | Article |
| id | doaj-art-8390f3de094b4b51a429ecf125ee52d6 |
| institution | DOAJ |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2015-03-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-8390f3de094b4b51a429ecf125ee52d62025-08-20T02:56:39ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982015-03-0115716074Investigation of a Two-Grid Method of Improved Accuracy for the Elliptic Reaction–Diffusion Equation with Boundary LayersS.V. Tikhovskaya0Sobolev Institute of Mathematics, Omsk Branch, Omsk, 644099 RussiaA two-grid method for the elliptic equation with a small parameter ε multiplying the highest derivative is investigated. The ε-uniformly convergent difference scheme on the Shishkin mesh is considered. To resolve the difference scheme, a two-grid method with ε-uniform interpolation formula is used. To increase the accuracy of the scheme, the Richardson extrapolation in the two-grid method is applied. The results of numerical experiments are discussed. Various iterative methods for implementation of the two-grid algorithm are suggested.https://kpfu.ru/portal/docs/F_887599187/157_1_phys_mat_7.pdfelliptic reaction–diffusion equationsingular perturbationshishkin meshtwogrid methodrichardson extrapolationuniform convergence |
| spellingShingle | S.V. Tikhovskaya Investigation of a Two-Grid Method of Improved Accuracy for the Elliptic Reaction–Diffusion Equation with Boundary Layers Учёные записки Казанского университета: Серия Физико-математические науки elliptic reaction–diffusion equation singular perturbation shishkin mesh twogrid method richardson extrapolation uniform convergence |
| title | Investigation of a Two-Grid Method of Improved Accuracy for the Elliptic Reaction–Diffusion Equation with Boundary Layers |
| title_full | Investigation of a Two-Grid Method of Improved Accuracy for the Elliptic Reaction–Diffusion Equation with Boundary Layers |
| title_fullStr | Investigation of a Two-Grid Method of Improved Accuracy for the Elliptic Reaction–Diffusion Equation with Boundary Layers |
| title_full_unstemmed | Investigation of a Two-Grid Method of Improved Accuracy for the Elliptic Reaction–Diffusion Equation with Boundary Layers |
| title_short | Investigation of a Two-Grid Method of Improved Accuracy for the Elliptic Reaction–Diffusion Equation with Boundary Layers |
| title_sort | investigation of a two grid method of improved accuracy for the elliptic reaction diffusion equation with boundary layers |
| topic | elliptic reaction–diffusion equation singular perturbation shishkin mesh twogrid method richardson extrapolation uniform convergence |
| url | https://kpfu.ru/portal/docs/F_887599187/157_1_phys_mat_7.pdf |
| work_keys_str_mv | AT svtikhovskaya investigationofatwogridmethodofimprovedaccuracyfortheellipticreactiondiffusionequationwithboundarylayers |