Adomian solution of a nonlinear quadratic integral equation
We are concerned here with a nonlinear quadratic integral equation (QIE). The existence of a unique solution will be proved. Convergence analysis of Adomian decomposition method (ADM) applied to these type of equations is discussed. Convergence analysis is reliable enough to estimate the maximum abs...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2013-04-01
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| Series: | Journal of the Egyptian Mathematical Society |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X12000582 |
| _version_ | 1818217474413297664 |
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| author | E.A.A. Ziada |
| author_facet | E.A.A. Ziada |
| author_sort | E.A.A. Ziada |
| collection | DOAJ |
| description | We are concerned here with a nonlinear quadratic integral equation (QIE). The existence of a unique solution will be proved. Convergence analysis of Adomian decomposition method (ADM) applied to these type of equations is discussed. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of Adomian’s series solution. Two methods are used to solve these type of equations; ADM and repeated trapezoidal method. The obtained results are compared. |
| first_indexed | 2024-12-12T07:08:26Z |
| format | Article |
| id | doaj.art-0d488746c9664523819a12e1638719ad |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-12T07:08:26Z |
| publishDate | 2013-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-0d488746c9664523819a12e1638719ad2022-12-22T00:33:40ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2013-04-01211525610.1016/j.joems.2012.11.001Adomian solution of a nonlinear quadratic integral equationE.A.A. ZiadaWe are concerned here with a nonlinear quadratic integral equation (QIE). The existence of a unique solution will be proved. Convergence analysis of Adomian decomposition method (ADM) applied to these type of equations is discussed. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of Adomian’s series solution. Two methods are used to solve these type of equations; ADM and repeated trapezoidal method. The obtained results are compared.http://www.sciencedirect.com/science/article/pii/S1110256X12000582Nonlinear quadratic integral equationBanach spaceFixed point theoremConvergence analysisAdomian methodRepeated trapezoidal method |
| spellingShingle | E.A.A. Ziada Adomian solution of a nonlinear quadratic integral equation Journal of the Egyptian Mathematical Society Nonlinear quadratic integral equation Banach space Fixed point theorem Convergence analysis Adomian method Repeated trapezoidal method |
| title | Adomian solution of a nonlinear quadratic integral equation |
| title_full | Adomian solution of a nonlinear quadratic integral equation |
| title_fullStr | Adomian solution of a nonlinear quadratic integral equation |
| title_full_unstemmed | Adomian solution of a nonlinear quadratic integral equation |
| title_short | Adomian solution of a nonlinear quadratic integral equation |
| title_sort | adomian solution of a nonlinear quadratic integral equation |
| topic | Nonlinear quadratic integral equation Banach space Fixed point theorem Convergence analysis Adomian method Repeated trapezoidal method |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X12000582 |
| work_keys_str_mv | AT eaaziada adomiansolutionofanonlinearquadraticintegralequation |