On fully discrete collocation methods for solving weakly singular integral equations
A popular class of methods for solving weakly singular integral equations is the class of piecewise polynomial collocation methods. In order to implement those methods one has to compute exactly certain integrals that determine the linear system to be solved. Unfortunately those integrals usually ca...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2009-03-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/6521 |
| _version_ | 1818386687265341440 |
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| author | Raul Kangro Inga Kangro |
| author_facet | Raul Kangro Inga Kangro |
| author_sort | Raul Kangro |
| collection | DOAJ |
| description | A popular class of methods for solving weakly singular integral equations is the class of piecewise polynomial collocation methods. In order to implement those methods one has to compute exactly certain integrals that determine the linear system to be solved. Unfortunately those integrals usually cannot be computed exactly and even when analytic formulas exist, their straightforward application may cause unacceptable roundoff errors resulting in apparent instability of those methods in the case of highly nonuniform grids. In this paper fully discrete analogs of the collocation methods, where integrals are replaced by quadrature formulas, are considered, corresponding error estimates are derived.
First published online: 14 Oct 2010 |
| first_indexed | 2024-12-14T03:58:00Z |
| format | Article |
| id | doaj.art-7c84bc6cbf3c4c38835258297a569014 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-14T03:58:00Z |
| publishDate | 2009-03-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-7c84bc6cbf3c4c38835258297a5690142022-12-21T23:18:02ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102009-03-0114110.3846/1392-6292.2009.14.69-78On fully discrete collocation methods for solving weakly singular integral equationsRaul Kangro0Inga Kangro1Institute of Mathematical Statistics, University of Tartu; Liivi 2-513, 50409, Tartu, EstoniaInstitute of Cybernetics, Tallinn University of Technology; Akadeemia 21, 12618, Tallinn, EstoniaA popular class of methods for solving weakly singular integral equations is the class of piecewise polynomial collocation methods. In order to implement those methods one has to compute exactly certain integrals that determine the linear system to be solved. Unfortunately those integrals usually cannot be computed exactly and even when analytic formulas exist, their straightforward application may cause unacceptable roundoff errors resulting in apparent instability of those methods in the case of highly nonuniform grids. In this paper fully discrete analogs of the collocation methods, where integrals are replaced by quadrature formulas, are considered, corresponding error estimates are derived. First published online: 14 Oct 2010https://journals.vgtu.lt/index.php/MMA/article/view/6521weakly singularintegral equationcollocation methodnonuniform gridfully discrete methodFredholm equation |
| spellingShingle | Raul Kangro Inga Kangro On fully discrete collocation methods for solving weakly singular integral equations Mathematical Modelling and Analysis weakly singular integral equation collocation method nonuniform grid fully discrete method Fredholm equation |
| title | On fully discrete collocation methods for solving weakly singular integral equations |
| title_full | On fully discrete collocation methods for solving weakly singular integral equations |
| title_fullStr | On fully discrete collocation methods for solving weakly singular integral equations |
| title_full_unstemmed | On fully discrete collocation methods for solving weakly singular integral equations |
| title_short | On fully discrete collocation methods for solving weakly singular integral equations |
| title_sort | on fully discrete collocation methods for solving weakly singular integral equations |
| topic | weakly singular integral equation collocation method nonuniform grid fully discrete method Fredholm equation |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/6521 |
| work_keys_str_mv | AT raulkangro onfullydiscretecollocationmethodsforsolvingweaklysingularintegralequations AT ingakangro onfullydiscretecollocationmethodsforsolvingweaklysingularintegralequations |