The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals
We investigate the numerical solutions of nonlinear Volterra integral equations by the block-by-block method especially useful for the solution of integral equations on large-size intervals. A convergence theorem is proved showing that the method has at least sixth order of convergence. Finally, the...
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| Published in: | Український математичний журнал |
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| Date: | 2012 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Український математичний журнал
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/164448 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals / R. Katani, S. Shahmorad // Український математичний журнал. — 2012. — Т. 64, № 7. — С. 919-931. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862706205764354048 |
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| author | Katani, R. Shahmorad, S. |
| author_facet | Katani, R. Shahmorad, S. |
| citation_txt | The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals / R. Katani, S. Shahmorad // Український математичний журнал. — 2012. — Т. 64, № 7. — С. 919-931. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний журнал |
| description | We investigate the numerical solutions of nonlinear Volterra integral equations by the block-by-block method especially useful for the solution of integral equations on large-size intervals. A convergence theorem is proved showing that the method has at least sixth order of convergence. Finally, the performance of the method is illustrated by some numerical examples.
Дослiджено чисельний розв’язок нелiнiйних iнтегральних рiвнянь Вольтерра поблочним методом, який є особливо корисним при розв’язуваннi iнтегральних рiвнянь на великих iнтервалах. Доведено теорему про збiжнiсть, яка показує, що цей метод має щонайменше шостий порядок збiжностi. Дiю методу проiлюстровано на кiлькох числових прикладах.
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| first_indexed | 2025-12-07T16:57:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-164448 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1027-3190 |
| language | English |
| last_indexed | 2025-12-07T16:57:51Z |
| publishDate | 2012 |
| publisher | Український математичний журнал |
| record_format | dspace |
| spelling | Katani, R. Shahmorad, S. 2020-02-09T15:34:48Z 2020-02-09T15:34:48Z 2012 The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals / R. Katani, S. Shahmorad // Український математичний журнал. — 2012. — Т. 64, № 7. — С. 919-931. — Бібліогр.: 14 назв. — англ. 1027-3190 https://nasplib.isofts.kiev.ua/handle/123456789/164448 517.9 We investigate the numerical solutions of nonlinear Volterra integral equations by the block-by-block method especially useful for the solution of integral equations on large-size intervals. A convergence theorem is proved showing that the method has at least sixth order of convergence. Finally, the performance of the method is illustrated by some numerical examples. Дослiджено чисельний розв’язок нелiнiйних iнтегральних рiвнянь Вольтерра поблочним методом, який є особливо корисним при розв’язуваннi iнтегральних рiвнянь на великих iнтервалах. Доведено теорему про збiжнiсть, яка показує, що цей метод має щонайменше шостий порядок збiжностi. Дiю методу проiлюстровано на кiлькох числових прикладах. en Український математичний журнал Український математичний журнал Статті The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals Поблочний метод iз квадратурою ромберга для розв’язування нелiнiйних iнтегральних рiвнянь Вольтерра на великих iнтервалах Article published earlier |
| spellingShingle | The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals Katani, R. Shahmorad, S. Статті |
| title | The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals |
| title_alt | Поблочний метод iз квадратурою ромберга для розв’язування нелiнiйних iнтегральних рiвнянь Вольтерра на великих iнтервалах |
| title_full | The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals |
| title_fullStr | The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals |
| title_full_unstemmed | The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals |
| title_short | The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals |
| title_sort | block-by-block method with romberg quadrature for the solution of nonlinear volterra integral equations on large intervals |
| topic | Статті |
| topic_facet | Статті |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/164448 |
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