On the solution of multi-dimensional nonlinear integral equation with modified newton method
In this note, multi-dimensional nonlinear integral equations (multi-dimensional NIEs) in R n is considered. Implementing modified Newton method (Modified NM) reduces multi-dimensional NIEs into multi-dimensional linear integral equations (multi-dimensional LIEs), which can be solved by discritizatio...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Scientific Publishers
2017
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/62585/ http://psasir.upm.edu.my/id/eprint/62585/1/NEWTON.pdf |
| _version_ | 1848854639907176448 |
|---|---|
| author | Hameed, Hameed Husam Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri |
| author_facet | Hameed, Hameed Husam Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri |
| author_sort | Hameed, Hameed Husam |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this note, multi-dimensional nonlinear integral equations (multi-dimensional NIEs) in R n is considered. Implementing modified Newton method (Modified NM) reduces multi-dimensional NIEs into multi-dimensional linear integral equations (multi-dimensional LIEs), which can be solved by discritization method. Quadrature method together with collocation are used to find values of unknown functions. Existence and uniqueness solution of the problems are shown. The rate of convergence of the proposed method is proved using the principle of majorant function. Finally, numerical examples are provided and it reveals that proposed method is both accurate and effective as well as comparisons with other methods are also presented. |
| first_indexed | 2025-11-15T11:13:04Z |
| format | Article |
| id | upm-62585 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:13:04Z |
| publishDate | 2017 |
| publisher | American Scientific Publishers |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-625852020-12-03T20:51:44Z http://psasir.upm.edu.my/id/eprint/62585/ On the solution of multi-dimensional nonlinear integral equation with modified newton method Hameed, Hameed Husam Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri In this note, multi-dimensional nonlinear integral equations (multi-dimensional NIEs) in R n is considered. Implementing modified Newton method (Modified NM) reduces multi-dimensional NIEs into multi-dimensional linear integral equations (multi-dimensional LIEs), which can be solved by discritization method. Quadrature method together with collocation are used to find values of unknown functions. Existence and uniqueness solution of the problems are shown. The rate of convergence of the proposed method is proved using the principle of majorant function. Finally, numerical examples are provided and it reveals that proposed method is both accurate and effective as well as comparisons with other methods are also presented. American Scientific Publishers 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/62585/1/NEWTON.pdf Hameed, Hameed Husam and Eshkuvatov, Zainidin K. and Nik Long, Nik Mohd Asri (2017) On the solution of multi-dimensional nonlinear integral equation with modified newton method. Journal of Computational and Theoretical Nanoscience, 14 (11). 5298 - 5303. ISSN 1546-1955; ESSN: 1546-1963 https://www.ingentaconnect.com/content/asp/jctn/2017/00000014/00000011/art00021;jsessionid=5bjtgh44o3v0.x-ic-live-03 10.1166/jctn.2017.6938 |
| spellingShingle | Hameed, Hameed Husam Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri On the solution of multi-dimensional nonlinear integral equation with modified newton method |
| title | On the solution of multi-dimensional nonlinear integral equation with modified newton method |
| title_full | On the solution of multi-dimensional nonlinear integral equation with modified newton method |
| title_fullStr | On the solution of multi-dimensional nonlinear integral equation with modified newton method |
| title_full_unstemmed | On the solution of multi-dimensional nonlinear integral equation with modified newton method |
| title_short | On the solution of multi-dimensional nonlinear integral equation with modified newton method |
| title_sort | on the solution of multi-dimensional nonlinear integral equation with modified newton method |
| url | http://psasir.upm.edu.my/id/eprint/62585/ http://psasir.upm.edu.my/id/eprint/62585/ http://psasir.upm.edu.my/id/eprint/62585/ http://psasir.upm.edu.my/id/eprint/62585/1/NEWTON.pdf |