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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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Український математичний журнал
2012
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| Назва видання: | Український математичний журнал |
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| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/164448 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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| id |
irk-123456789-164448 |
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irk-123456789-1644482020-02-10T01:28:15Z The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals Katani, R. Shahmorad, S. Статті 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. 2012 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/164448 517.9 en Український математичний журнал Український математичний журнал |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Статті Статті |
| spellingShingle |
Статті Статті Katani, R. Shahmorad, S. The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals 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. |
| format |
Article |
| author |
Katani, R. Shahmorad, S. |
| author_facet |
Katani, R. Shahmorad, S. |
| author_sort |
Katani, R. |
| title |
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_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_sort |
block-by-block method with romberg quadrature for the solution of nonlinear volterra integral equations on large intervals |
| publisher |
Український математичний журнал |
| publishDate |
2012 |
| topic_facet |
Статті |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/164448 |
| 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. |
| series |
Український математичний журнал |
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