Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes
This work is devoted to Fredholm integral equations of second kind with non-separable kernels. Our strategy is to approximate the non-separable kernel by using an adequate Taylor’s development. Then, we adapt an already known technique used for separable kernels to our case. First, we study the loca...
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| Format: | Article |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1747 |
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| author | José Manuel Gutiérrez Miguel Ángel Hernández-Verón Eulalia Martínez |
| author_facet | José Manuel Gutiérrez Miguel Ángel Hernández-Verón Eulalia Martínez |
| author_sort | José Manuel Gutiérrez |
| collection | DOAJ |
| description | This work is devoted to Fredholm integral equations of second kind with non-separable kernels. Our strategy is to approximate the non-separable kernel by using an adequate Taylor’s development. Then, we adapt an already known technique used for separable kernels to our case. First, we study the local convergence of the proposed iterative scheme, so we obtain a ball of starting points around the solution. Then, we complete the theoretical study with the semilocal convergence analysis, that allow us to obtain the domain of existence for the solution in terms of the starting point. In this case, the existence of a solution is deduced. Finally, we illustrate this study with some numerical experiments. |
| first_indexed | 2024-03-10T15:43:22Z |
| format | Article |
| id | doaj.art-5bd2b32c50104df4929c3f3233ecf42b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:43:22Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5bd2b32c50104df4929c3f3233ecf42b2023-11-20T16:39:49ZengMDPI AGMathematics2227-73902020-10-01810174710.3390/math8101747Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative SchemesJosé Manuel Gutiérrez0Miguel Ángel Hernández-Verón1Eulalia Martínez2Department of Mathematics and Computation, University of La Rioja, 26006 Logroño, SpainDepartment of Mathematics and Computation, University of La Rioja, 26006 Logroño, SpainInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 València, SpainThis work is devoted to Fredholm integral equations of second kind with non-separable kernels. Our strategy is to approximate the non-separable kernel by using an adequate Taylor’s development. Then, we adapt an already known technique used for separable kernels to our case. First, we study the local convergence of the proposed iterative scheme, so we obtain a ball of starting points around the solution. Then, we complete the theoretical study with the semilocal convergence analysis, that allow us to obtain the domain of existence for the solution in terms of the starting point. In this case, the existence of a solution is deduced. Finally, we illustrate this study with some numerical experiments.https://www.mdpi.com/2227-7390/8/10/1747Fredholm integral equationiterative processesNewton’s methodseparable and non-separable kernelslocal and semilocal convergence |
| spellingShingle | José Manuel Gutiérrez Miguel Ángel Hernández-Verón Eulalia Martínez Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes Mathematics Fredholm integral equation iterative processes Newton’s method separable and non-separable kernels local and semilocal convergence |
| title | Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes |
| title_full | Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes |
| title_fullStr | Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes |
| title_full_unstemmed | Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes |
| title_short | Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes |
| title_sort | improved iterative solution of linear fredholm integral equations of second kind via inverse free iterative schemes |
| topic | Fredholm integral equation iterative processes Newton’s method separable and non-separable kernels local and semilocal convergence |
| url | https://www.mdpi.com/2227-7390/8/10/1747 |
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