Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations
In this paper an application of the homotopy analysis method for some type of nonlinear and linear integral equations of the second kind is presented. A special case of considered equation is the Volterra- Fredholm integral equation. In homotopy analysis method a series is created. It has shown that...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Edyta Hetmaniok [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Journal of numerical mathematics - Berlin : de Gruyter, 2002, 23(2015), 4, Seite 331-344 |
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| Übergeordnetes Werk: |
volume:23 ; year:2015 ; number:4 ; pages:331-344 |
| Links: |
|---|
| DOI / URN: |
10.1515/jnma-2015-0022 |
|---|
| Katalog-ID: |
OLC1959723057 |
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| 520 | |a In this paper an application of the homotopy analysis method for some type of nonlinear and linear integral equations of the second kind is presented. A special case of considered equation is the Volterra- Fredholm integral equation. In homotopy analysis method a series is created. It has shown that if the series is convergent, its sum is the solution of the considered equation. It has been also shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in homotopy analysis method is convergent. The error of the approximate solution was estimated. This approximate solution is obtained when we limit to the partial sum of the series.Application of the method is illustrated with examples. | ||
| 650 | 4 | |a Volterra-Fredholm integral equation | |
| 650 | 4 | |a nonlinear integral equation | |
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| 700 | 0 | |a Damian Słota |4 oth | |
| 700 | 0 | |a Roman Wituła |4 oth | |
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10.1515/jnma-2015-0022 doi PQ20160617 (DE-627)OLC1959723057 (DE-599)GBVOLC1959723057 (PRQ)p1644-923cdc455e8cd0ed01ed07cd126f77e080efad771404a4ff60b9d6d6cb5051a70 (KEY)0231802420150000023000400331convergenceanderrorestimationofhomotopyanalysismet DE-627 ger DE-627 rakwb eng 510 DNB Edyta Hetmaniok verfasserin aut Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper an application of the homotopy analysis method for some type of nonlinear and linear integral equations of the second kind is presented. A special case of considered equation is the Volterra- Fredholm integral equation. In homotopy analysis method a series is created. It has shown that if the series is convergent, its sum is the solution of the considered equation. It has been also shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in homotopy analysis method is convergent. The error of the approximate solution was estimated. This approximate solution is obtained when we limit to the partial sum of the series.Application of the method is illustrated with examples. Volterra-Fredholm integral equation nonlinear integral equation linear integral equation convergence Homotopy analysis method error estimations Convergence Integral equations Iwona Nowak oth Damian Słota oth Roman Wituła oth Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 23(2015), 4, Seite 331-344 (DE-627)349238499 (DE-600)2080770-3 (DE-576)099427869 1570-2820 nnns volume:23 year:2015 number:4 pages:331-344 http://dx.doi.org/10.1515/jnma-2015-0022 Volltext http://www.degruyter.com/doi/10.1515/jnma-2015-0022 http://search.proquest.com/docview/1748185213 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2012 GBV_ILN_4277 GBV_ILN_4700 AR 23 2015 4 331-344 |
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10.1515/jnma-2015-0022 doi PQ20160617 (DE-627)OLC1959723057 (DE-599)GBVOLC1959723057 (PRQ)p1644-923cdc455e8cd0ed01ed07cd126f77e080efad771404a4ff60b9d6d6cb5051a70 (KEY)0231802420150000023000400331convergenceanderrorestimationofhomotopyanalysismet DE-627 ger DE-627 rakwb eng 510 DNB Edyta Hetmaniok verfasserin aut Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper an application of the homotopy analysis method for some type of nonlinear and linear integral equations of the second kind is presented. A special case of considered equation is the Volterra- Fredholm integral equation. In homotopy analysis method a series is created. It has shown that if the series is convergent, its sum is the solution of the considered equation. It has been also shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in homotopy analysis method is convergent. The error of the approximate solution was estimated. This approximate solution is obtained when we limit to the partial sum of the series.Application of the method is illustrated with examples. Volterra-Fredholm integral equation nonlinear integral equation linear integral equation convergence Homotopy analysis method error estimations Convergence Integral equations Iwona Nowak oth Damian Słota oth Roman Wituła oth Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 23(2015), 4, Seite 331-344 (DE-627)349238499 (DE-600)2080770-3 (DE-576)099427869 1570-2820 nnns volume:23 year:2015 number:4 pages:331-344 http://dx.doi.org/10.1515/jnma-2015-0022 Volltext http://www.degruyter.com/doi/10.1515/jnma-2015-0022 http://search.proquest.com/docview/1748185213 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2012 GBV_ILN_4277 GBV_ILN_4700 AR 23 2015 4 331-344 |
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10.1515/jnma-2015-0022 doi PQ20160617 (DE-627)OLC1959723057 (DE-599)GBVOLC1959723057 (PRQ)p1644-923cdc455e8cd0ed01ed07cd126f77e080efad771404a4ff60b9d6d6cb5051a70 (KEY)0231802420150000023000400331convergenceanderrorestimationofhomotopyanalysismet DE-627 ger DE-627 rakwb eng 510 DNB Edyta Hetmaniok verfasserin aut Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper an application of the homotopy analysis method for some type of nonlinear and linear integral equations of the second kind is presented. A special case of considered equation is the Volterra- Fredholm integral equation. In homotopy analysis method a series is created. It has shown that if the series is convergent, its sum is the solution of the considered equation. It has been also shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in homotopy analysis method is convergent. The error of the approximate solution was estimated. This approximate solution is obtained when we limit to the partial sum of the series.Application of the method is illustrated with examples. Volterra-Fredholm integral equation nonlinear integral equation linear integral equation convergence Homotopy analysis method error estimations Convergence Integral equations Iwona Nowak oth Damian Słota oth Roman Wituła oth Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 23(2015), 4, Seite 331-344 (DE-627)349238499 (DE-600)2080770-3 (DE-576)099427869 1570-2820 nnns volume:23 year:2015 number:4 pages:331-344 http://dx.doi.org/10.1515/jnma-2015-0022 Volltext http://www.degruyter.com/doi/10.1515/jnma-2015-0022 http://search.proquest.com/docview/1748185213 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2012 GBV_ILN_4277 GBV_ILN_4700 AR 23 2015 4 331-344 |
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10.1515/jnma-2015-0022 doi PQ20160617 (DE-627)OLC1959723057 (DE-599)GBVOLC1959723057 (PRQ)p1644-923cdc455e8cd0ed01ed07cd126f77e080efad771404a4ff60b9d6d6cb5051a70 (KEY)0231802420150000023000400331convergenceanderrorestimationofhomotopyanalysismet DE-627 ger DE-627 rakwb eng 510 DNB Edyta Hetmaniok verfasserin aut Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper an application of the homotopy analysis method for some type of nonlinear and linear integral equations of the second kind is presented. A special case of considered equation is the Volterra- Fredholm integral equation. In homotopy analysis method a series is created. It has shown that if the series is convergent, its sum is the solution of the considered equation. It has been also shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in homotopy analysis method is convergent. The error of the approximate solution was estimated. This approximate solution is obtained when we limit to the partial sum of the series.Application of the method is illustrated with examples. Volterra-Fredholm integral equation nonlinear integral equation linear integral equation convergence Homotopy analysis method error estimations Convergence Integral equations Iwona Nowak oth Damian Słota oth Roman Wituła oth Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 23(2015), 4, Seite 331-344 (DE-627)349238499 (DE-600)2080770-3 (DE-576)099427869 1570-2820 nnns volume:23 year:2015 number:4 pages:331-344 http://dx.doi.org/10.1515/jnma-2015-0022 Volltext http://www.degruyter.com/doi/10.1515/jnma-2015-0022 http://search.proquest.com/docview/1748185213 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2012 GBV_ILN_4277 GBV_ILN_4700 AR 23 2015 4 331-344 |
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10.1515/jnma-2015-0022 doi PQ20160617 (DE-627)OLC1959723057 (DE-599)GBVOLC1959723057 (PRQ)p1644-923cdc455e8cd0ed01ed07cd126f77e080efad771404a4ff60b9d6d6cb5051a70 (KEY)0231802420150000023000400331convergenceanderrorestimationofhomotopyanalysismet DE-627 ger DE-627 rakwb eng 510 DNB Edyta Hetmaniok verfasserin aut Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper an application of the homotopy analysis method for some type of nonlinear and linear integral equations of the second kind is presented. A special case of considered equation is the Volterra- Fredholm integral equation. In homotopy analysis method a series is created. It has shown that if the series is convergent, its sum is the solution of the considered equation. It has been also shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in homotopy analysis method is convergent. The error of the approximate solution was estimated. This approximate solution is obtained when we limit to the partial sum of the series.Application of the method is illustrated with examples. Volterra-Fredholm integral equation nonlinear integral equation linear integral equation convergence Homotopy analysis method error estimations Convergence Integral equations Iwona Nowak oth Damian Słota oth Roman Wituła oth Enthalten in Journal of numerical mathematics Berlin : de Gruyter, 2002 23(2015), 4, Seite 331-344 (DE-627)349238499 (DE-600)2080770-3 (DE-576)099427869 1570-2820 nnns volume:23 year:2015 number:4 pages:331-344 http://dx.doi.org/10.1515/jnma-2015-0022 Volltext http://www.degruyter.com/doi/10.1515/jnma-2015-0022 http://search.proquest.com/docview/1748185213 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2012 GBV_ILN_4277 GBV_ILN_4700 AR 23 2015 4 331-344 |
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convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations |
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Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations |
| abstract |
In this paper an application of the homotopy analysis method for some type of nonlinear and linear integral equations of the second kind is presented. A special case of considered equation is the Volterra- Fredholm integral equation. In homotopy analysis method a series is created. It has shown that if the series is convergent, its sum is the solution of the considered equation. It has been also shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in homotopy analysis method is convergent. The error of the approximate solution was estimated. This approximate solution is obtained when we limit to the partial sum of the series.Application of the method is illustrated with examples. |
| abstractGer |
In this paper an application of the homotopy analysis method for some type of nonlinear and linear integral equations of the second kind is presented. A special case of considered equation is the Volterra- Fredholm integral equation. In homotopy analysis method a series is created. It has shown that if the series is convergent, its sum is the solution of the considered equation. It has been also shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in homotopy analysis method is convergent. The error of the approximate solution was estimated. This approximate solution is obtained when we limit to the partial sum of the series.Application of the method is illustrated with examples. |
| abstract_unstemmed |
In this paper an application of the homotopy analysis method for some type of nonlinear and linear integral equations of the second kind is presented. A special case of considered equation is the Volterra- Fredholm integral equation. In homotopy analysis method a series is created. It has shown that if the series is convergent, its sum is the solution of the considered equation. It has been also shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in homotopy analysis method is convergent. The error of the approximate solution was estimated. This approximate solution is obtained when we limit to the partial sum of the series.Application of the method is illustrated with examples. |
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| title_short |
Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations |
| url |
http://dx.doi.org/10.1515/jnma-2015-0022 http://www.degruyter.com/doi/10.1515/jnma-2015-0022 http://search.proquest.com/docview/1748185213 |
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Iwona Nowak Damian Słota Roman Wituła |
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| doi_str |
10.1515/jnma-2015-0022 |
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2024-07-03T18:31:44.976Z |
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