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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Kazan Federal University
2015-03-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://kpfu.ru/portal/docs/F_887599187/157_1_phys_mat_7.pdf |
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| Summary: | 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. |
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| ISSN: | 2541-7746 2500-2198 |