Picard-Reproducing Kernel Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-Emden Type Equations
An iterative method is discussed with respect to its effectiveness and capability of solving singular nonlinear Lane-Emden type equations using reproducing kernel Hilbert space method combined with the Picard iteration. Some new error estimates for application of the method are established. We prove...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2015-11-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/1033 |
| _version_ | 1818888136258748416 |
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| author | Babak Azarnavid Foroud Parvaneh Saeid Abbasbandy |
| author_facet | Babak Azarnavid Foroud Parvaneh Saeid Abbasbandy |
| author_sort | Babak Azarnavid |
| collection | DOAJ |
| description | An iterative method is discussed with respect to its effectiveness and capability of solving singular nonlinear Lane-Emden type equations using reproducing kernel Hilbert space method combined with the Picard iteration. Some new error estimates for application of the method are established. We prove the convergence of the combined method. The numerical examples demonstrates a good agreement between numerical results and analytical predictions. |
| first_indexed | 2024-12-19T16:48:19Z |
| format | Article |
| id | doaj.art-24841270560e4fab974b47e109e32a32 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-19T16:48:19Z |
| publishDate | 2015-11-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-24841270560e4fab974b47e109e32a322022-12-21T20:13:35ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102015-11-0120610.3846/13926292.2015.1111953Picard-Reproducing Kernel Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-Emden Type EquationsBabak Azarnavid0Foroud Parvaneh1Saeid Abbasbandy2Department of Mathematics, Imam Khomeini International University, 34149-16818 Ghazvin, IranDepartment of Science, Kermanshah Branch, Islamic Azad University, Kermanshah, IranDepartment of Mathematics, Imam Khomeini International University, 34149-16818 Ghazvin, IranAn iterative method is discussed with respect to its effectiveness and capability of solving singular nonlinear Lane-Emden type equations using reproducing kernel Hilbert space method combined with the Picard iteration. Some new error estimates for application of the method are established. We prove the convergence of the combined method. The numerical examples demonstrates a good agreement between numerical results and analytical predictions.https://journals.vgtu.lt/index.php/MMA/article/view/1033reproducing kernel Hilbert spacePicard iterationerror estimateconvergencesingular nonlinear Lane-Emden type equations |
| spellingShingle | Babak Azarnavid Foroud Parvaneh Saeid Abbasbandy Picard-Reproducing Kernel Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-Emden Type Equations Mathematical Modelling and Analysis reproducing kernel Hilbert space Picard iteration error estimate convergence singular nonlinear Lane-Emden type equations |
| title | Picard-Reproducing Kernel Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-Emden Type Equations |
| title_full | Picard-Reproducing Kernel Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-Emden Type Equations |
| title_fullStr | Picard-Reproducing Kernel Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-Emden Type Equations |
| title_full_unstemmed | Picard-Reproducing Kernel Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-Emden Type Equations |
| title_short | Picard-Reproducing Kernel Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-Emden Type Equations |
| title_sort | picard reproducing kernel hilbert space method for solving generalized singular nonlinear lane emden type equations |
| topic | reproducing kernel Hilbert space Picard iteration error estimate convergence singular nonlinear Lane-Emden type equations |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/1033 |
| work_keys_str_mv | AT babakazarnavid picardreproducingkernelhilbertspacemethodforsolvinggeneralizedsingularnonlinearlaneemdentypeequations AT foroudparvaneh picardreproducingkernelhilbertspacemethodforsolvinggeneralizedsingularnonlinearlaneemdentypeequations AT saeidabbasbandy picardreproducingkernelhilbertspacemethodforsolvinggeneralizedsingularnonlinearlaneemdentypeequations |