Numerical Investigation of the Fredholm Integral Equations with Oscillatory Kernels Based on Compactly Supported Radial Basis Functions

The integral equations with oscillatory kernels are of great concern in applied sciences and computational engineering, particularly for large-scale data points and high frequencies. Therefore, the interest of this work is to develop an accurate, efficient, and stable algorithm for the computation o...
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Autor*in:	Suliman Khan [verfasserIn] Sharifah E. Alhazmi [verfasserIn] Aisha M. Alqahtani [verfasserIn] Ahmed EI-Sayed Ahmed [verfasserIn] Mansour F. Yaseen [verfasserIn] Elsayed M. Tag-Eldin [verfasserIn] Dania Qaiser [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	compactly supported radial basis functions fredholm integral equations levin method stability analysis highly oscillatory kernels high frequency

Übergeordnetes Werk:	In: Symmetry - MDPI AG, 2009, 14(2022), 8, p 1527
Übergeordnetes Werk:	volume:14 ; year:2022 ; number:8, p 1527

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/sym14081527

Katalog-ID:	DOAJ087187612

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520			\|a The integral equations with oscillatory kernels are of great concern in applied sciences and computational engineering, particularly for large-scale data points and high frequencies. Therefore, the interest of this work is to develop an accurate, efficient, and stable algorithm for the computation of the Fredholm integral equations (FIEs) with the oscillatory kernel. The oscillatory part of the FIEs is evaluated by the Levin quadrature coupled with a compactly supported radial basis function (CS-RBF). The algorithm exhibits sparse and well-conditioned matrix even for large-scale data points, as compared to its counterpart, multi-quadric radial basis function (MQ-RBF) coupled with the Levin quadrature. Usually, the RBFs behave with spherical symmetry about the centers, known as radial. The comparison of convergence and stability analysis of both types of RBFs are performed and numerically verified. The proposed algorithm is tested with benchmark problems and compared with the counterpart methods in the literature. It is concluded that the algorithm in this work is accurate, robust, and stable than the existing methods in the literature based on MQ-RBF and the Chebyshev interpolation matrix.
650		4	\|a compactly supported radial basis functions
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allfields	10.3390/sym14081527 doi (DE-627)DOAJ087187612 (DE-599)DOAJ1ec6acf9cdd74faa815712ca548df5e1 DE-627 ger DE-627 rakwb eng QA1-939 Suliman Khan verfasserin aut Numerical Investigation of the Fredholm Integral Equations with Oscillatory Kernels Based on Compactly Supported Radial Basis Functions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The integral equations with oscillatory kernels are of great concern in applied sciences and computational engineering, particularly for large-scale data points and high frequencies. Therefore, the interest of this work is to develop an accurate, efficient, and stable algorithm for the computation of the Fredholm integral equations (FIEs) with the oscillatory kernel. The oscillatory part of the FIEs is evaluated by the Levin quadrature coupled with a compactly supported radial basis function (CS-RBF). The algorithm exhibits sparse and well-conditioned matrix even for large-scale data points, as compared to its counterpart, multi-quadric radial basis function (MQ-RBF) coupled with the Levin quadrature. Usually, the RBFs behave with spherical symmetry about the centers, known as radial. The comparison of convergence and stability analysis of both types of RBFs are performed and numerically verified. The proposed algorithm is tested with benchmark problems and compared with the counterpart methods in the literature. It is concluded that the algorithm in this work is accurate, robust, and stable than the existing methods in the literature based on MQ-RBF and the Chebyshev interpolation matrix. compactly supported radial basis functions fredholm integral equations levin method stability analysis highly oscillatory kernels high frequency Mathematics Sharifah E. Alhazmi verfasserin aut Aisha M. Alqahtani verfasserin aut Ahmed EI-Sayed Ahmed verfasserin aut Mansour F. Yaseen verfasserin aut Elsayed M. Tag-Eldin verfasserin aut Dania Qaiser verfasserin aut In Symmetry MDPI AG, 2009 14(2022), 8, p 1527 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:14 year:2022 number:8, p 1527 https://doi.org/10.3390/sym14081527 kostenfrei https://doaj.org/article/1ec6acf9cdd74faa815712ca548df5e1 kostenfrei https://www.mdpi.com/2073-8994/14/8/1527 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2022 8, p 1527
spelling	10.3390/sym14081527 doi (DE-627)DOAJ087187612 (DE-599)DOAJ1ec6acf9cdd74faa815712ca548df5e1 DE-627 ger DE-627 rakwb eng QA1-939 Suliman Khan verfasserin aut Numerical Investigation of the Fredholm Integral Equations with Oscillatory Kernels Based on Compactly Supported Radial Basis Functions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The integral equations with oscillatory kernels are of great concern in applied sciences and computational engineering, particularly for large-scale data points and high frequencies. Therefore, the interest of this work is to develop an accurate, efficient, and stable algorithm for the computation of the Fredholm integral equations (FIEs) with the oscillatory kernel. The oscillatory part of the FIEs is evaluated by the Levin quadrature coupled with a compactly supported radial basis function (CS-RBF). The algorithm exhibits sparse and well-conditioned matrix even for large-scale data points, as compared to its counterpart, multi-quadric radial basis function (MQ-RBF) coupled with the Levin quadrature. Usually, the RBFs behave with spherical symmetry about the centers, known as radial. The comparison of convergence and stability analysis of both types of RBFs are performed and numerically verified. The proposed algorithm is tested with benchmark problems and compared with the counterpart methods in the literature. It is concluded that the algorithm in this work is accurate, robust, and stable than the existing methods in the literature based on MQ-RBF and the Chebyshev interpolation matrix. compactly supported radial basis functions fredholm integral equations levin method stability analysis highly oscillatory kernels high frequency Mathematics Sharifah E. Alhazmi verfasserin aut Aisha M. Alqahtani verfasserin aut Ahmed EI-Sayed Ahmed verfasserin aut Mansour F. Yaseen verfasserin aut Elsayed M. Tag-Eldin verfasserin aut Dania Qaiser verfasserin aut In Symmetry MDPI AG, 2009 14(2022), 8, p 1527 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:14 year:2022 number:8, p 1527 https://doi.org/10.3390/sym14081527 kostenfrei https://doaj.org/article/1ec6acf9cdd74faa815712ca548df5e1 kostenfrei https://www.mdpi.com/2073-8994/14/8/1527 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2022 8, p 1527
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allfieldsSound	10.3390/sym14081527 doi (DE-627)DOAJ087187612 (DE-599)DOAJ1ec6acf9cdd74faa815712ca548df5e1 DE-627 ger DE-627 rakwb eng QA1-939 Suliman Khan verfasserin aut Numerical Investigation of the Fredholm Integral Equations with Oscillatory Kernels Based on Compactly Supported Radial Basis Functions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The integral equations with oscillatory kernels are of great concern in applied sciences and computational engineering, particularly for large-scale data points and high frequencies. Therefore, the interest of this work is to develop an accurate, efficient, and stable algorithm for the computation of the Fredholm integral equations (FIEs) with the oscillatory kernel. The oscillatory part of the FIEs is evaluated by the Levin quadrature coupled with a compactly supported radial basis function (CS-RBF). The algorithm exhibits sparse and well-conditioned matrix even for large-scale data points, as compared to its counterpart, multi-quadric radial basis function (MQ-RBF) coupled with the Levin quadrature. Usually, the RBFs behave with spherical symmetry about the centers, known as radial. The comparison of convergence and stability analysis of both types of RBFs are performed and numerically verified. The proposed algorithm is tested with benchmark problems and compared with the counterpart methods in the literature. It is concluded that the algorithm in this work is accurate, robust, and stable than the existing methods in the literature based on MQ-RBF and the Chebyshev interpolation matrix. compactly supported radial basis functions fredholm integral equations levin method stability analysis highly oscillatory kernels high frequency Mathematics Sharifah E. Alhazmi verfasserin aut Aisha M. Alqahtani verfasserin aut Ahmed EI-Sayed Ahmed verfasserin aut Mansour F. Yaseen verfasserin aut Elsayed M. Tag-Eldin verfasserin aut Dania Qaiser verfasserin aut In Symmetry MDPI AG, 2009 14(2022), 8, p 1527 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:14 year:2022 number:8, p 1527 https://doi.org/10.3390/sym14081527 kostenfrei https://doaj.org/article/1ec6acf9cdd74faa815712ca548df5e1 kostenfrei https://www.mdpi.com/2073-8994/14/8/1527 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2022 8, p 1527
language	English
source	In Symmetry 14(2022), 8, p 1527 volume:14 year:2022 number:8, p 1527
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topic_facet	compactly supported radial basis functions fredholm integral equations levin method stability analysis highly oscillatory kernels high frequency Mathematics
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authorswithroles_txt_mv	Suliman Khan @@aut@@ Sharifah E. Alhazmi @@aut@@ Aisha M. Alqahtani @@aut@@ Ahmed EI-Sayed Ahmed @@aut@@ Mansour F. Yaseen @@aut@@ Elsayed M. Tag-Eldin @@aut@@ Dania Qaiser @@aut@@
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callnumber-first	Q - Science
author	Suliman Khan
spellingShingle	Suliman Khan misc QA1-939 misc compactly supported radial basis functions misc fredholm integral equations misc levin method misc stability analysis misc highly oscillatory kernels misc high frequency misc Mathematics Numerical Investigation of the Fredholm Integral Equations with Oscillatory Kernels Based on Compactly Supported Radial Basis Functions
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topic_title	QA1-939 Numerical Investigation of the Fredholm Integral Equations with Oscillatory Kernels Based on Compactly Supported Radial Basis Functions compactly supported radial basis functions fredholm integral equations levin method stability analysis highly oscillatory kernels high frequency
topic	misc QA1-939 misc compactly supported radial basis functions misc fredholm integral equations misc levin method misc stability analysis misc highly oscillatory kernels misc high frequency misc Mathematics
topic_unstemmed	misc QA1-939 misc compactly supported radial basis functions misc fredholm integral equations misc levin method misc stability analysis misc highly oscillatory kernels misc high frequency misc Mathematics
topic_browse	misc QA1-939 misc compactly supported radial basis functions misc fredholm integral equations misc levin method misc stability analysis misc highly oscillatory kernels misc high frequency misc Mathematics
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title	Numerical Investigation of the Fredholm Integral Equations with Oscillatory Kernels Based on Compactly Supported Radial Basis Functions
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title_full	Numerical Investigation of the Fredholm Integral Equations with Oscillatory Kernels Based on Compactly Supported Radial Basis Functions
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title_sort	numerical investigation of the fredholm integral equations with oscillatory kernels based on compactly supported radial basis functions
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title_auth	Numerical Investigation of the Fredholm Integral Equations with Oscillatory Kernels Based on Compactly Supported Radial Basis Functions
abstract	The integral equations with oscillatory kernels are of great concern in applied sciences and computational engineering, particularly for large-scale data points and high frequencies. Therefore, the interest of this work is to develop an accurate, efficient, and stable algorithm for the computation of the Fredholm integral equations (FIEs) with the oscillatory kernel. The oscillatory part of the FIEs is evaluated by the Levin quadrature coupled with a compactly supported radial basis function (CS-RBF). The algorithm exhibits sparse and well-conditioned matrix even for large-scale data points, as compared to its counterpart, multi-quadric radial basis function (MQ-RBF) coupled with the Levin quadrature. Usually, the RBFs behave with spherical symmetry about the centers, known as radial. The comparison of convergence and stability analysis of both types of RBFs are performed and numerically verified. The proposed algorithm is tested with benchmark problems and compared with the counterpart methods in the literature. It is concluded that the algorithm in this work is accurate, robust, and stable than the existing methods in the literature based on MQ-RBF and the Chebyshev interpolation matrix.
abstractGer	The integral equations with oscillatory kernels are of great concern in applied sciences and computational engineering, particularly for large-scale data points and high frequencies. Therefore, the interest of this work is to develop an accurate, efficient, and stable algorithm for the computation of the Fredholm integral equations (FIEs) with the oscillatory kernel. The oscillatory part of the FIEs is evaluated by the Levin quadrature coupled with a compactly supported radial basis function (CS-RBF). The algorithm exhibits sparse and well-conditioned matrix even for large-scale data points, as compared to its counterpart, multi-quadric radial basis function (MQ-RBF) coupled with the Levin quadrature. Usually, the RBFs behave with spherical symmetry about the centers, known as radial. The comparison of convergence and stability analysis of both types of RBFs are performed and numerically verified. The proposed algorithm is tested with benchmark problems and compared with the counterpart methods in the literature. It is concluded that the algorithm in this work is accurate, robust, and stable than the existing methods in the literature based on MQ-RBF and the Chebyshev interpolation matrix.
abstract_unstemmed	The integral equations with oscillatory kernels are of great concern in applied sciences and computational engineering, particularly for large-scale data points and high frequencies. Therefore, the interest of this work is to develop an accurate, efficient, and stable algorithm for the computation of the Fredholm integral equations (FIEs) with the oscillatory kernel. The oscillatory part of the FIEs is evaluated by the Levin quadrature coupled with a compactly supported radial basis function (CS-RBF). The algorithm exhibits sparse and well-conditioned matrix even for large-scale data points, as compared to its counterpart, multi-quadric radial basis function (MQ-RBF) coupled with the Levin quadrature. Usually, the RBFs behave with spherical symmetry about the centers, known as radial. The comparison of convergence and stability analysis of both types of RBFs are performed and numerically verified. The proposed algorithm is tested with benchmark problems and compared with the counterpart methods in the literature. It is concluded that the algorithm in this work is accurate, robust, and stable than the existing methods in the literature based on MQ-RBF and the Chebyshev interpolation matrix.
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title_short	Numerical Investigation of the Fredholm Integral Equations with Oscillatory Kernels Based on Compactly Supported Radial Basis Functions
url	https://doi.org/10.3390/sym14081527 https://doaj.org/article/1ec6acf9cdd74faa815712ca548df5e1 https://www.mdpi.com/2073-8994/14/8/1527 https://doaj.org/toc/2073-8994
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up_date	2024-07-04T00:37:53.514Z
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Numerical Investigation of the Fredholm Integral Equations with Oscillatory Kernels Based on Compactly Supported Radial Basis Functions

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