A Newton-like method for the numerical solution of nonlinear Fredholm-type operator equations
In a recent paper, Hernández and Salanova proposed an interesting Newton-like method for the solution of nonlinear Fredholm integral equations. The aim of the present paper is to carry over this method to nonlinear operator equations of similar type. By using a functional analytic approach, the pres...
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| Vydané v: | Applied mathematics and computation Ročník 218; číslo 20; s. 10129 - 10148 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Inc
15.06.2012
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | In a recent paper, Hernández and Salanova proposed an interesting Newton-like method for the solution of nonlinear Fredholm integral equations. The aim of the present paper is to carry over this method to nonlinear operator equations of similar type. By using a functional analytic approach, the presentation becomes much clearer and more general. Apart from this, some new results in the Banach space setting as well as in the applications are obtained. |
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| AbstractList | In a recent paper, Hernández and Salanova proposed an interesting Newton-like method for the solution of nonlinear Fredholm integral equations. The aim of the present paper is to carry over this method to nonlinear operator equations of similar type. By using a functional analytic approach, the presentation becomes much clearer and more general. Apart from this, some new results in the Banach space setting as well as in the applications are obtained. In a recent paper, HernA!ndez and Salanova proposed an interesting Newton-like method for the solution of nonlinear Fredholm integral equations. The aim of the present paper is to carry over this method to nonlinear operator equations of similar type. By using a functional analytic approach, the presentation becomes much clearer and more general. Apart from this, some new results in the Banach space setting as well as in the applications are obtained. |
| Author | Kohaupt, L. |
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| Keywords | Nonlinear Fredholm-type operator equation Nonlinear Fredholm integral equation Newton-like method Newton method Method of successive approximations |
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| References | Kantorovich, Akilov (b0010) 1982 Hernández, Salanova (b0005) 2005; 17 Krasosel’skij, Lifshits, Sobolev (b0015) 1989 Ortega, Rheinboldt (b0025) 1970 Krasosel’skii, Vainikko, Zabreiko, Rutitskii, Stetsenko (b0020) 1972 Ortega (10.1016/j.amc.2012.03.089_b0025) 1970 Krasosel’skii (10.1016/j.amc.2012.03.089_b0020) 1972 Hernández (10.1016/j.amc.2012.03.089_b0005) 2005; 17 Kantorovich (10.1016/j.amc.2012.03.089_b0010) 1982 Krasosel’skij (10.1016/j.amc.2012.03.089_b0015) 1989 |
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| Snippet | In a recent paper, Hernández and Salanova proposed an interesting Newton-like method for the solution of nonlinear Fredholm integral equations. The aim of the... In a recent paper, HernA!ndez and Salanova proposed an interesting Newton-like method for the solution of nonlinear Fredholm integral equations. The aim of the... |
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| SubjectTerms | Banach space Computation Integral equations Mathematical analysis Mathematical models Method of successive approximations Newton method Newton methods Newton-like method Nonlinear Fredholm integral equation Nonlinear Fredholm-type operator equation Nonlinearity Operators |
| Title | A Newton-like method for the numerical solution of nonlinear Fredholm-type operator equations |
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