A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems.
[EN]In this paper, we solve linear boundary value problems of second-order in ordinary differential equations with the generalized finite difference method and compare the numerical accuracy for different orders of approximations. We develop a strategy for dealing with ill-conditioned stars based on...
| Authors: | ; ; |
|---|---|
| Format: | Article |
| Status: | Published version |
| Publication date: | 2021 |
| Country: | España |
| Institution: | Universidad de Salamanca (USAL) |
| Repository: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/156717 |
| Online Access: | http://hdl.handle.net/10366/156717 |
| Access Level: | Open access |
| Keyword: | Fourth-order approximations Generalized finite difference method ill-conditioned stars Parallel processing 12 Matemáticas |
| _version_ | 1878733746747736064 |
|---|---|
| author | Albuquerque‐Ferreira, Augusto C. |
| author2 | Ureña, Miguel Ramos Calle, Higinio |
| author2_role | author author |
| author_browse | Albuquerque‐Ferreira, Augusto C. Ramos Calle, Higinio Ureña, Miguel |
| author_facet | Albuquerque‐Ferreira, Augusto C. Ureña, Miguel Ramos Calle, Higinio |
| author_role | author |
| collection | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| description | [EN]In this paper, we solve linear boundary value problems of second-order in ordinary differential equations with the generalized finite difference method and compare the numerical accuracy for different orders of approximations. We develop a strategy for dealing with ill-conditioned stars based on the condition number of the matrix of derivatives. In addition, we consider a scheme implemented with parallel processing for the formation of the stars and the calculation of the derivatives. We present some examples with high gradients in irregular discretizations exaggerated on purpose, to highlight the efficiency of the proposed strategy. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_5c2ff5d69a984e66e94c4bbcdd5fa534 |
| institution | Universidad de Salamanca (USAL) |
| instname_str | Universidad de Salamanca (USAL) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:gredos.usal.es:10366/156717 |
| publishDate | 2021 |
| publishDateSort | 2021 |
| publisher | Wiley |
| publisherStr | Wiley |
| reponame_str | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| spelling | A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems. Albuquerque‐Ferreira, Augusto C. Ureña, Miguel Ramos Calle, Higinio Fourth-order approximations Generalized finite difference method ill-conditioned stars Parallel processing 12 Matemáticas [EN]In this paper, we solve linear boundary value problems of second-order in ordinary differential equations with the generalized finite difference method and compare the numerical accuracy for different orders of approximations. We develop a strategy for dealing with ill-conditioned stars based on the condition number of the matrix of derivatives. In addition, we consider a scheme implemented with parallel processing for the formation of the stars and the calculation of the derivatives. We present some examples with high gradients in irregular discretizations exaggerated on purpose, to highlight the efficiency of the proposed strategy. Wiley http://hdl.handle.net/10366/156717 |
| spellingShingle | A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems. Albuquerque‐Ferreira, Augusto C. Fourth-order approximations Generalized finite difference method ill-conditioned stars Parallel processing 12 Matemáticas |
| status_str | publishedVersion |
| title | A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems. |
| title_full | A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems. |
| title_fullStr | A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems. |
| title_full_unstemmed | A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems. |
| title_short | A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems. |
| title_sort | A strategy to avoid ill‐conditioned stars in the generalized finite difference method for solving one‐dimensional problems. |
| topic | Fourth-order approximations Generalized finite difference method ill-conditioned stars Parallel processing 12 Matemáticas |
| topic_facet | Fourth-order approximations Generalized finite difference method ill-conditioned stars Parallel processing 12 Matemáticas |
| url | http://hdl.handle.net/10366/156717 |