Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels

In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The oth...
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Autor*in:	Chunhua Fang [verfasserIn] Guo He [verfasserIn] Shuhuang Xiang [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Volterra integral equations highly oscillatory Bessel kernel Hermite interpolation direct Hermite collocation method piecewise Hermite collocation method

Übergeordnetes Werk:	In: Symmetry - MDPI AG, 2009, 11(2019), 2, p 168
Übergeordnetes Werk:	volume:11 ; year:2019 ; number:2, p 168

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/sym11020168

Katalog-ID:	DOAJ022812172

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520			\|a In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The other one is piecewise Hermite collocation method, which used a two-points Hermite interpolation in each subinterval. These two methods can calculate the approximate value of function value and derivative value simultaneously. Both methods are constructed easily and implemented well by the fast computation of highly oscillatory integrals involving Bessel functions. Under some conditions, the asymptotic convergence order with respect to oscillatory factor of these two methods are established, which are higher than the existing results. Some numerical experiments are included to show efficiency of these two methods.
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spelling	10.3390/sym11020168 doi (DE-627)DOAJ022812172 (DE-599)DOAJ1749c2ed449f4c4ab8efbbdfcb8e779a DE-627 ger DE-627 rakwb eng QA1-939 Chunhua Fang verfasserin aut Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The other one is piecewise Hermite collocation method, which used a two-points Hermite interpolation in each subinterval. These two methods can calculate the approximate value of function value and derivative value simultaneously. Both methods are constructed easily and implemented well by the fast computation of highly oscillatory integrals involving Bessel functions. Under some conditions, the asymptotic convergence order with respect to oscillatory factor of these two methods are established, which are higher than the existing results. Some numerical experiments are included to show efficiency of these two methods. Volterra integral equations highly oscillatory Bessel kernel Hermite interpolation direct Hermite collocation method piecewise Hermite collocation method Mathematics Guo He verfasserin aut Shuhuang Xiang verfasserin aut In Symmetry MDPI AG, 2009 11(2019), 2, p 168 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:11 year:2019 number:2, p 168 https://doi.org/10.3390/sym11020168 kostenfrei https://doaj.org/article/1749c2ed449f4c4ab8efbbdfcb8e779a kostenfrei https://www.mdpi.com/2073-8994/11/2/168 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 11 2019 2, p 168
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allfieldsGer	10.3390/sym11020168 doi (DE-627)DOAJ022812172 (DE-599)DOAJ1749c2ed449f4c4ab8efbbdfcb8e779a DE-627 ger DE-627 rakwb eng QA1-939 Chunhua Fang verfasserin aut Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The other one is piecewise Hermite collocation method, which used a two-points Hermite interpolation in each subinterval. These two methods can calculate the approximate value of function value and derivative value simultaneously. Both methods are constructed easily and implemented well by the fast computation of highly oscillatory integrals involving Bessel functions. Under some conditions, the asymptotic convergence order with respect to oscillatory factor of these two methods are established, which are higher than the existing results. Some numerical experiments are included to show efficiency of these two methods. Volterra integral equations highly oscillatory Bessel kernel Hermite interpolation direct Hermite collocation method piecewise Hermite collocation method Mathematics Guo He verfasserin aut Shuhuang Xiang verfasserin aut In Symmetry MDPI AG, 2009 11(2019), 2, p 168 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:11 year:2019 number:2, p 168 https://doi.org/10.3390/sym11020168 kostenfrei https://doaj.org/article/1749c2ed449f4c4ab8efbbdfcb8e779a kostenfrei https://www.mdpi.com/2073-8994/11/2/168 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 11 2019 2, p 168
allfieldsSound	10.3390/sym11020168 doi (DE-627)DOAJ022812172 (DE-599)DOAJ1749c2ed449f4c4ab8efbbdfcb8e779a DE-627 ger DE-627 rakwb eng QA1-939 Chunhua Fang verfasserin aut Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The other one is piecewise Hermite collocation method, which used a two-points Hermite interpolation in each subinterval. These two methods can calculate the approximate value of function value and derivative value simultaneously. Both methods are constructed easily and implemented well by the fast computation of highly oscillatory integrals involving Bessel functions. Under some conditions, the asymptotic convergence order with respect to oscillatory factor of these two methods are established, which are higher than the existing results. Some numerical experiments are included to show efficiency of these two methods. Volterra integral equations highly oscillatory Bessel kernel Hermite interpolation direct Hermite collocation method piecewise Hermite collocation method Mathematics Guo He verfasserin aut Shuhuang Xiang verfasserin aut In Symmetry MDPI AG, 2009 11(2019), 2, p 168 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:11 year:2019 number:2, p 168 https://doi.org/10.3390/sym11020168 kostenfrei https://doaj.org/article/1749c2ed449f4c4ab8efbbdfcb8e779a kostenfrei https://www.mdpi.com/2073-8994/11/2/168 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 11 2019 2, p 168
language	English
source	In Symmetry 11(2019), 2, p 168 volume:11 year:2019 number:2, p 168
sourceStr	In Symmetry 11(2019), 2, p 168 volume:11 year:2019 number:2, p 168
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Volterra integral equations highly oscillatory Bessel kernel Hermite interpolation direct Hermite collocation method piecewise Hermite collocation method Mathematics
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container_title	Symmetry
authorswithroles_txt_mv	Chunhua Fang @@aut@@ Guo He @@aut@@ Shuhuang Xiang @@aut@@
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callnumber-first	Q - Science
author	Chunhua Fang
spellingShingle	Chunhua Fang misc QA1-939 misc Volterra integral equations misc highly oscillatory Bessel kernel misc Hermite interpolation misc direct Hermite collocation method misc piecewise Hermite collocation method misc Mathematics Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels
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topic_title	QA1-939 Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels Volterra integral equations highly oscillatory Bessel kernel Hermite interpolation direct Hermite collocation method piecewise Hermite collocation method
topic	misc QA1-939 misc Volterra integral equations misc highly oscillatory Bessel kernel misc Hermite interpolation misc direct Hermite collocation method misc piecewise Hermite collocation method misc Mathematics
topic_unstemmed	misc QA1-939 misc Volterra integral equations misc highly oscillatory Bessel kernel misc Hermite interpolation misc direct Hermite collocation method misc piecewise Hermite collocation method misc Mathematics
topic_browse	misc QA1-939 misc Volterra integral equations misc highly oscillatory Bessel kernel misc Hermite interpolation misc direct Hermite collocation method misc piecewise Hermite collocation method misc Mathematics
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title	Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels
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title_full	Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels
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title_sort	hermite-type collocation methods to solve volterra integral equations with highly oscillatory bessel kernels
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title_auth	Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels
abstract	In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The other one is piecewise Hermite collocation method, which used a two-points Hermite interpolation in each subinterval. These two methods can calculate the approximate value of function value and derivative value simultaneously. Both methods are constructed easily and implemented well by the fast computation of highly oscillatory integrals involving Bessel functions. Under some conditions, the asymptotic convergence order with respect to oscillatory factor of these two methods are established, which are higher than the existing results. Some numerical experiments are included to show efficiency of these two methods.
abstractGer	In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The other one is piecewise Hermite collocation method, which used a two-points Hermite interpolation in each subinterval. These two methods can calculate the approximate value of function value and derivative value simultaneously. Both methods are constructed easily and implemented well by the fast computation of highly oscillatory integrals involving Bessel functions. Under some conditions, the asymptotic convergence order with respect to oscillatory factor of these two methods are established, which are higher than the existing results. Some numerical experiments are included to show efficiency of these two methods.
abstract_unstemmed	In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The other one is piecewise Hermite collocation method, which used a two-points Hermite interpolation in each subinterval. These two methods can calculate the approximate value of function value and derivative value simultaneously. Both methods are constructed easily and implemented well by the fast computation of highly oscillatory integrals involving Bessel functions. Under some conditions, the asymptotic convergence order with respect to oscillatory factor of these two methods are established, which are higher than the existing results. Some numerical experiments are included to show efficiency of these two methods.
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title_short	Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels
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Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels

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