Using modified two-dimensional block-pulse functions for the numerical solution of nonlinear two-dimensional volterra integral equations
In this paper, the Modified two-dimensional block-pulse functions (M2D-BFs) are used as a new set of basis functions for expanding two-dimensional functions. The main properties of M2DBFs are determined and an operational matrix for integration obtained. M2D-BFs are used to solve nonlinear two-dimen...
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| Format: | Article |
| Language: | English |
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University of Mohaghegh Ardabili
2014-06-01
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| Series: | Journal of Hyperstructures |
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| Online Access: | https://jhs.uma.ac.ir/article_2574_444426e0dd61aade21dafbc365af614d.pdf |
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| author | F. Mirzaee Elham Hadadiyan |
| author_facet | F. Mirzaee Elham Hadadiyan |
| author_sort | F. Mirzaee |
| collection | DOAJ |
| description | In this paper, the Modified two-dimensional block-pulse functions (M2D-BFs) are used as a new set of basis functions for expanding two-dimensional functions. The main properties of M2DBFs are determined and an operational matrix for integration obtained. M2D-BFs are used to solve nonlinear two-dimensional Volterra integral equations of the first kind. Some theorems are included to show convergence and advantage of the method. Finally, numerical examples is presented to show the efficiency and accuracy of the method. |
| format | Article |
| id | doaj-art-c76fb1969a2345f1bdd19c014c581747 |
| institution | Kabale University |
| issn | 2251-8436 2322-1666 |
| language | English |
| publishDate | 2014-06-01 |
| publisher | University of Mohaghegh Ardabili |
| record_format | Article |
| series | Journal of Hyperstructures |
| spelling | doaj-art-c76fb1969a2345f1bdd19c014c5817472025-08-20T03:28:48ZengUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-84362322-16662014-06-0131688010.22098/jhs.2014.25742574Using modified two-dimensional block-pulse functions for the numerical solution of nonlinear two-dimensional volterra integral equationsF. Mirzaee0Elham Hadadiyan1Department of Mathematics, Faculty of Science, Malayer University, Malayer, 65719- 95863, Iran.Department of Mathematics, Faculty of Science, Malayer University, Malayer, 65719- 95863, Iran.In this paper, the Modified two-dimensional block-pulse functions (M2D-BFs) are used as a new set of basis functions for expanding two-dimensional functions. The main properties of M2DBFs are determined and an operational matrix for integration obtained. M2D-BFs are used to solve nonlinear two-dimensional Volterra integral equations of the first kind. Some theorems are included to show convergence and advantage of the method. Finally, numerical examples is presented to show the efficiency and accuracy of the method.https://jhs.uma.ac.ir/article_2574_444426e0dd61aade21dafbc365af614d.pdfnonlinear two-dimensional volterra integral equationsblock-pulse functionsoperational matrix |
| spellingShingle | F. Mirzaee Elham Hadadiyan Using modified two-dimensional block-pulse functions for the numerical solution of nonlinear two-dimensional volterra integral equations Journal of Hyperstructures nonlinear two-dimensional volterra integral equations block-pulse functions operational matrix |
| title | Using modified two-dimensional block-pulse functions for the numerical solution of nonlinear two-dimensional volterra integral equations |
| title_full | Using modified two-dimensional block-pulse functions for the numerical solution of nonlinear two-dimensional volterra integral equations |
| title_fullStr | Using modified two-dimensional block-pulse functions for the numerical solution of nonlinear two-dimensional volterra integral equations |
| title_full_unstemmed | Using modified two-dimensional block-pulse functions for the numerical solution of nonlinear two-dimensional volterra integral equations |
| title_short | Using modified two-dimensional block-pulse functions for the numerical solution of nonlinear two-dimensional volterra integral equations |
| title_sort | using modified two dimensional block pulse functions for the numerical solution of nonlinear two dimensional volterra integral equations |
| topic | nonlinear two-dimensional volterra integral equations block-pulse functions operational matrix |
| url | https://jhs.uma.ac.ir/article_2574_444426e0dd61aade21dafbc365af614d.pdf |
| work_keys_str_mv | AT fmirzaee usingmodifiedtwodimensionalblockpulsefunctionsforthenumericalsolutionofnonlineartwodimensionalvolterraintegralequations AT elhamhadadiyan usingmodifiedtwodimensionalblockpulsefunctionsforthenumericalsolutionofnonlineartwodimensionalvolterraintegralequations |