A Picard-Type Iterative Scheme for Fredholm Integral Equations of the Second Kind
In this work, we present an application of Newton’s method for solving nonlinear equations in Banach spaces to a particular problem: the approximation of the inverse operators that appear in the solution of Fredholm integral equations. Therefore, we construct an iterative method with quadratic conve...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/1/83 |
| _version_ | 1827698652245655552 |
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| author | José M. Gutiérrez Miguel Á. Hernández-Verón |
| author_facet | José M. Gutiérrez Miguel Á. Hernández-Verón |
| author_sort | José M. Gutiérrez |
| collection | DOAJ |
| description | In this work, we present an application of Newton’s method for solving nonlinear equations in Banach spaces to a particular problem: the approximation of the inverse operators that appear in the solution of Fredholm integral equations. Therefore, we construct an iterative method with quadratic convergence that does not use either derivatives or inverse operators. Consequently, this new procedure is especially useful for solving non-homogeneous Fredholm integral equations of the first kind. We combine this method with a technique to find the solution of Fredholm integral equations with separable kernels to obtain a procedure that allows us to approach the solution when the kernel is non-separable. |
| first_indexed | 2024-03-10T13:34:14Z |
| format | Article |
| id | doaj.art-c5146606b5e9474db3478a69dd2a9ddf |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T13:34:14Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c5146606b5e9474db3478a69dd2a9ddf2023-11-21T07:42:19ZengMDPI AGMathematics2227-73902021-01-01918310.3390/math9010083A Picard-Type Iterative Scheme for Fredholm Integral Equations of the Second KindJosé M. Gutiérrez0Miguel Á. Hernández-Verón1Department of Mathematics and Computer Sciences, University of La Rioja, 26006 Logroño, SpainDepartment of Mathematics and Computer Sciences, University of La Rioja, 26006 Logroño, SpainIn this work, we present an application of Newton’s method for solving nonlinear equations in Banach spaces to a particular problem: the approximation of the inverse operators that appear in the solution of Fredholm integral equations. Therefore, we construct an iterative method with quadratic convergence that does not use either derivatives or inverse operators. Consequently, this new procedure is especially useful for solving non-homogeneous Fredholm integral equations of the first kind. We combine this method with a technique to find the solution of Fredholm integral equations with separable kernels to obtain a procedure that allows us to approach the solution when the kernel is non-separable.https://www.mdpi.com/2227-7390/9/1/83Fredholm integral equationNewton’s methoditerative processes |
| spellingShingle | José M. Gutiérrez Miguel Á. Hernández-Verón A Picard-Type Iterative Scheme for Fredholm Integral Equations of the Second Kind Mathematics Fredholm integral equation Newton’s method iterative processes |
| title | A Picard-Type Iterative Scheme for Fredholm Integral Equations of the Second Kind |
| title_full | A Picard-Type Iterative Scheme for Fredholm Integral Equations of the Second Kind |
| title_fullStr | A Picard-Type Iterative Scheme for Fredholm Integral Equations of the Second Kind |
| title_full_unstemmed | A Picard-Type Iterative Scheme for Fredholm Integral Equations of the Second Kind |
| title_short | A Picard-Type Iterative Scheme for Fredholm Integral Equations of the Second Kind |
| title_sort | picard type iterative scheme for fredholm integral equations of the second kind |
| topic | Fredholm integral equation Newton’s method iterative processes |
| url | https://www.mdpi.com/2227-7390/9/1/83 |
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