A new approach of shifted Jacobi spectral Galerkin methods (SJSGM) for weakly singular Fredholm integral equation with non-smooth solution
This article presents a new approach of shifted Jacobi spectral Galerkin methods to solve weakly singular Fredholm integral equations with non-smooth solutions. We have incorporated the singular part of the kernel into a single Jacobi weight function, by dividing the integration into two parts and u...
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| Published in: | Numerical algorithms Vol. 96; no. 4; pp. 1553 - 1582 |
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01.08.2024
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| ISSN: | 1017-1398, 1572-9265 |
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| Abstract | This article presents a new approach of shifted Jacobi spectral Galerkin methods to solve weakly singular Fredholm integral equations with non-smooth solutions. We have incorporated the singular part of the kernel into a single Jacobi weight function, by dividing the integration into two parts and using a simple variable transformation. Taking advantage of orthogonal projection operator and weighted inner product with respect to that same Jacobi weight function, we are able to obtain improved convergence rate for iterated shifted Jacobi spectral Galerkin method (SJSGM) and iterated shifted Jacobi spectral multi-Galerkin method (SJSMGM) in both weighted and infinity norms. Further, we obtain improved superconvergence rate for iterated SJSGM and iterated SJSMGM, by improving the regularity of exact solution, using smoothing transformation. Increasing the value of the smoothing parameter we can improve the regularity of the exact solution upto the desired degree. Numerical results with a comparative study of pre and post smoothing transformation are given to illustrate the theoretical results and efficiency of our proposed methods. |
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| AbstractList | This article presents a new approach of shifted Jacobi spectral Galerkin methods to solve weakly singular Fredholm integral equations with non-smooth solutions. We have incorporated the singular part of the kernel into a single Jacobi weight function, by dividing the integration into two parts and using a simple variable transformation. Taking advantage of orthogonal projection operator and weighted inner product with respect to that same Jacobi weight function, we are able to obtain improved convergence rate for iterated shifted Jacobi spectral Galerkin method (SJSGM) and iterated shifted Jacobi spectral multi-Galerkin method (SJSMGM) in both weighted and infinity norms. Further, we obtain improved superconvergence rate for iterated SJSGM and iterated SJSMGM, by improving the regularity of exact solution, using smoothing transformation. Increasing the value of the smoothing parameter we can improve the regularity of the exact solution upto the desired degree. Numerical results with a comparative study of pre and post smoothing transformation are given to illustrate the theoretical results and efficiency of our proposed methods. |
| Author | Mandal, Moumita Kayal, Arnab |
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| Cites_doi | 10.1216/jiea/1181076030 10.1090/S0025-5718-98-01005-9 10.3934/cpaa.2006.5.395 10.1017/S0004972700037916 10.1216/jiea/1181075816 10.1090/S0025-5718-1982-0669644-3 10.1007/978-3-540-30728-0 10.1016/j.amc.2018.01.046 10.3934/dcdss.2019043 10.1016/j.apnum.2006.07.007 10.1017/CBO9780511626340 10.1017/S0334270000002769 10.1016/j.amc.2021.126870 10.1007/978-3-642-97146-4 10.1016/j.cam.2010.01.033 10.1007/BF01404695 10.1007/s12190-013-0658-0 10.1137/070693308 10.1016/j.amc.2018.12.035 10.4171/zaa/501 10.2307/2007737 10.1090/S0002-9947-1970-0410210-0 10.1007/s00607-004-0088-9 10.1007/s11075-022-01376-x 10.1201/9781420035827 10.1063/1.1742352 10.1090/S0025-5718-1994-1218345-X 10.1007/BF01732317 10.1016/j.cam.2018.07.010 10.1016/j.cam.2018.09.032 |
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| Keywords | Jacobi polynomials Jacobi spectral Galerkin method Fredholm integral equations Superconvergence rate Weakly singular kernel |
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| References | YangYTangZHuangYNumerical solutions for Fredholm integral equations of the second kind with weakly singular kernel using spectral collocation methodAppl. Math. Comput.2019349314324389828110.1016/j.amc.2018.12.035 CaoYXuYSingularity preserving Galerkin methods for weakly singular Fredholm integral equationsJ. Integral Equations Appl.199463303334131251910.1216/jiea/1181075816 PedasAVainikkoGSuperconvergence of piecewise polynomial collocations for nonlinear weakly singular integral equationsJ. Integral Equations Appl.199794379406161431810.1216/jiea/1181076030 WangMMultistep collocation method for Fredholm integral equations of the second kindAppl. Math. Comput.2022420435763610.1016/j.amc.2021.126870 PedasAVainikkoGSmoothing transformation and piecewise polynomial collocation for weakly singular Volterra integral equationsComputing200473271293210625110.1007/s00607-004-0088-9 AtkinsonKThe numerical solution of Fredholm integral equations of the second kind with singular kernelsNumer. Math.197219324825930751210.1007/BF01404695 KressRLinear integral equations1989New YorkSpringer10.1007/978-3-642-97146-4 VainikkoGPedasAThe properties of solutions of weakly singular integral equationsThe ANZIAM Journal198122441943062693310.1017/S0334270000002769 SchneiderCProduct integration for weakly singular integral equationsMath. Comput.19813615320721359505310.2307/2007737 GrammontLKulkarniRPVasconcelosPBFast and accurate solvers for weakly singular integral equationsNumerical Algorithms20239220452070456288510.1007/s11075-022-01376-x RagozinDLPolynomial approximation on compact manifolds and homogeneous spacesTrans. Am. Math. Soc.19701501415341021010.1090/S0002-9947-1970-0410210-0 VainikkoEVainikkoGA spline product quasi-interpolation method for weakly singular Fredholm integral equationsSIAM J. Numer. Anal.200846417991820239939610.1137/070693308 PanigrahiBLNelakantiGLegendre Galerkin method for weakly singular Fredholm integral equations and the corresponding eigenvalue problemJ. Appl. Math. Comput.201343175197309639710.1007/s12190-013-0658-0 MonegatoGScuderiLHigh order methods for weakly singular integral equations with nonsmooth input functionsMath. Comput.19986722414931515160439510.1090/S0025-5718-98-01005-9 KulkarniRPA superconvergence result for solutions of compact operator equationsBull. Aust. Math. Soc.2003683517528202769410.1017/S0004972700037916 AuerPLGardnerCSNote on singular integral equations of the Kirkwood-Riseman typeJ. Chem. Phys.19552381545154610.1063/1.1742352 Canuto, C., Hussaini, M. Y., Quarteroni, A., Zang, T. A.: Spectral methods: fundamentals in single domains, Springer Science & Business Media (2007) Ahues, M., Largillier, A., Limaye, B.: Spectral computations for bounded operators, CRC press (2001) Orav-PuurandKPedasAVainikkoGNyström type methods for Fredholm integral equations with weak singularitiesJ. Comput. Appl. Math.2010234928482858265213010.1016/j.cam.2010.01.033 MandalMNelakantiGSuperconvergence results of Legendre spectral projection methods for weakly singular Fredholm-Hammerstein integral equationsJ. Comput. Appl. Math.2019349114131388670010.1016/j.cam.2018.09.032 PedasAVainikkoGSmoothing transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equationsCommun. Pure Appl. Anal.200652395413220010210.3934/cpaa.2006.5.395 KanekoHNorenRXuYRegularity of the solution of Hammerstein equations with weakly singular kernelIntegr. Eqn. Oper. Theory199013660670106612810.1007/BF01732317 Atkinson, K. E.: The numerical solution of integral equations of the second kind (Vol. 4), Cambridge university press (1997) PanigrahiBLMandalMNelakantiGLegendre multi-Galerkin methods for Fredholm integral equations with weakly singular kernel and the corresponding eigenvalue problemJ. Comput. Appl. Math.2019346224236386415710.1016/j.cam.2018.07.010 YangYHuangYSpectral Jacobi-Galerkin methods and iterated methods for Fredholm integral equations of the second kind with weakly singular kernelDiscrete Contin. Dyn. Syst. Ser. S.201912685702391777110.3934/dcdss.2019043 GrahamIGGalerkin methods for second kind integral equations with singularitiesMath. Comput.19823916051953366964410.1090/S0025-5718-1982-0669644-3 KanekoHXuYGauss-type quadratures for weakly singular integrals and their application to Fredholm integral equations of the second kindMath. Comput.199462206739753121834510.1090/S0025-5718-1994-1218345-X AllouchCSbibihDTahrichiMNumerical solutions of weakly singular Hammerstein integral equationsAppl. Math. Comput.2018329118128377331510.1016/j.amc.2018.01.046 PedasAVainikkoGThe smoothness of solutions to nonlinear weakly singular integral equationsZeitschrift für Analysis und ihre Anwendungen1994133463476129031410.4171/zaa/501 CaoYHuangMLiuLXuYHybrid collocation methods for Fredholm integral equations with weakly singular kernelsAppl. Numer. Math.2007575–7549561232243010.1016/j.apnum.2006.07.007 DL Ragozin (1677_CR24) 1970; 150 A Pedas (1677_CR21) 1997; 9 Y Cao (1677_CR7) 2007; 57 G Monegato (1677_CR16) 1998; 67 Y Cao (1677_CR8) 1994; 6 RP Kulkarni (1677_CR14) 2003; 68 M Wang (1677_CR28) 2022; 420 PL Auer (1677_CR5) 1955; 23 BL Panigrahi (1677_CR18) 2013; 43 E Vainikko (1677_CR27) 2008; 46 Y Yang (1677_CR29) 2019; 12 C Allouch (1677_CR2) 2018; 329 1677_CR6 G Vainikko (1677_CR26) 1981; 22 L Grammont (1677_CR10) 2023; 92 1677_CR4 1677_CR1 R Kress (1677_CR13) 1989 C Schneider (1677_CR25) 1981; 36 A Pedas (1677_CR23) 2006; 5 A Pedas (1677_CR20) 1994; 13 BL Panigrahi (1677_CR19) 2019; 346 K Orav-Puurand (1677_CR17) 2010; 234 Y Yang (1677_CR30) 2019; 349 IG Graham (1677_CR9) 1982; 39 A Pedas (1677_CR22) 2004; 73 H Kaneko (1677_CR12) 1994; 62 H Kaneko (1677_CR11) 1990; 13 K Atkinson (1677_CR3) 1972; 19 M Mandal (1677_CR15) 2019; 349 |
| References_xml | – reference: KulkarniRPA superconvergence result for solutions of compact operator equationsBull. Aust. Math. Soc.2003683517528202769410.1017/S0004972700037916 – reference: GrahamIGGalerkin methods for second kind integral equations with singularitiesMath. Comput.19823916051953366964410.1090/S0025-5718-1982-0669644-3 – reference: PedasAVainikkoGSuperconvergence of piecewise polynomial collocations for nonlinear weakly singular integral equationsJ. Integral Equations Appl.199794379406161431810.1216/jiea/1181076030 – reference: Canuto, C., Hussaini, M. Y., Quarteroni, A., Zang, T. A.: Spectral methods: fundamentals in single domains, Springer Science & Business Media (2007) – reference: VainikkoEVainikkoGA spline product quasi-interpolation method for weakly singular Fredholm integral equationsSIAM J. Numer. Anal.200846417991820239939610.1137/070693308 – reference: PedasAVainikkoGSmoothing transformation and piecewise polynomial collocation for weakly singular Volterra integral equationsComputing200473271293210625110.1007/s00607-004-0088-9 – reference: VainikkoGPedasAThe properties of solutions of weakly singular integral equationsThe ANZIAM Journal198122441943062693310.1017/S0334270000002769 – reference: AtkinsonKThe numerical solution of Fredholm integral equations of the second kind with singular kernelsNumer. Math.197219324825930751210.1007/BF01404695 – reference: PedasAVainikkoGThe smoothness of solutions to nonlinear weakly singular integral equationsZeitschrift für Analysis und ihre Anwendungen1994133463476129031410.4171/zaa/501 – reference: WangMMultistep collocation method for Fredholm integral equations of the second kindAppl. Math. Comput.2022420435763610.1016/j.amc.2021.126870 – reference: AuerPLGardnerCSNote on singular integral equations of the Kirkwood-Riseman typeJ. Chem. Phys.19552381545154610.1063/1.1742352 – reference: Orav-PuurandKPedasAVainikkoGNyström type methods for Fredholm integral equations with weak singularitiesJ. Comput. Appl. Math.2010234928482858265213010.1016/j.cam.2010.01.033 – reference: AllouchCSbibihDTahrichiMNumerical solutions of weakly singular Hammerstein integral equationsAppl. Math. Comput.2018329118128377331510.1016/j.amc.2018.01.046 – reference: MandalMNelakantiGSuperconvergence results of Legendre spectral projection methods for weakly singular Fredholm-Hammerstein integral equationsJ. Comput. Appl. Math.2019349114131388670010.1016/j.cam.2018.09.032 – reference: PanigrahiBLNelakantiGLegendre Galerkin method for weakly singular Fredholm integral equations and the corresponding eigenvalue problemJ. Appl. Math. Comput.201343175197309639710.1007/s12190-013-0658-0 – reference: Ahues, M., Largillier, A., Limaye, B.: Spectral computations for bounded operators, CRC press (2001) – reference: KressRLinear integral equations1989New YorkSpringer10.1007/978-3-642-97146-4 – reference: RagozinDLPolynomial approximation on compact manifolds and homogeneous spacesTrans. Am. Math. Soc.19701501415341021010.1090/S0002-9947-1970-0410210-0 – reference: PanigrahiBLMandalMNelakantiGLegendre multi-Galerkin methods for Fredholm integral equations with weakly singular kernel and the corresponding eigenvalue problemJ. Comput. Appl. Math.2019346224236386415710.1016/j.cam.2018.07.010 – reference: Atkinson, K. E.: The numerical solution of integral equations of the second kind (Vol. 4), Cambridge university press (1997) – reference: SchneiderCProduct integration for weakly singular integral equationsMath. Comput.19813615320721359505310.2307/2007737 – reference: KanekoHNorenRXuYRegularity of the solution of Hammerstein equations with weakly singular kernelIntegr. Eqn. Oper. Theory199013660670106612810.1007/BF01732317 – reference: YangYTangZHuangYNumerical solutions for Fredholm integral equations of the second kind with weakly singular kernel using spectral collocation methodAppl. Math. Comput.2019349314324389828110.1016/j.amc.2018.12.035 – reference: MonegatoGScuderiLHigh order methods for weakly singular integral equations with nonsmooth input functionsMath. Comput.19986722414931515160439510.1090/S0025-5718-98-01005-9 – reference: PedasAVainikkoGSmoothing transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equationsCommun. Pure Appl. Anal.200652395413220010210.3934/cpaa.2006.5.395 – reference: GrammontLKulkarniRPVasconcelosPBFast and accurate solvers for weakly singular integral equationsNumerical Algorithms20239220452070456288510.1007/s11075-022-01376-x – reference: KanekoHXuYGauss-type quadratures for weakly singular integrals and their application to Fredholm integral equations of the second kindMath. Comput.199462206739753121834510.1090/S0025-5718-1994-1218345-X – reference: YangYHuangYSpectral Jacobi-Galerkin methods and iterated methods for Fredholm integral equations of the second kind with weakly singular kernelDiscrete Contin. Dyn. Syst. Ser. S.201912685702391777110.3934/dcdss.2019043 – reference: CaoYHuangMLiuLXuYHybrid collocation methods for Fredholm integral equations with weakly singular kernelsAppl. Numer. Math.2007575–7549561232243010.1016/j.apnum.2006.07.007 – reference: CaoYXuYSingularity preserving Galerkin methods for weakly singular Fredholm integral equationsJ. Integral Equations Appl.199463303334131251910.1216/jiea/1181075816 – volume: 9 start-page: 379 issue: 4 year: 1997 ident: 1677_CR21 publication-title: J. Integral Equations Appl. doi: 10.1216/jiea/1181076030 – volume: 67 start-page: 1493 issue: 224 year: 1998 ident: 1677_CR16 publication-title: Math. Comput. doi: 10.1090/S0025-5718-98-01005-9 – volume: 5 start-page: 395 issue: 2 year: 2006 ident: 1677_CR23 publication-title: Commun. Pure Appl. Anal. doi: 10.3934/cpaa.2006.5.395 – volume: 68 start-page: 517 issue: 3 year: 2003 ident: 1677_CR14 publication-title: Bull. Aust. Math. Soc. doi: 10.1017/S0004972700037916 – volume: 6 start-page: 303 issue: 3 year: 1994 ident: 1677_CR8 publication-title: J. Integral Equations Appl. doi: 10.1216/jiea/1181075816 – volume: 39 start-page: 519 issue: 160 year: 1982 ident: 1677_CR9 publication-title: Math. Comput. doi: 10.1090/S0025-5718-1982-0669644-3 – ident: 1677_CR6 doi: 10.1007/978-3-540-30728-0 – volume: 329 start-page: 118 year: 2018 ident: 1677_CR2 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2018.01.046 – volume: 12 start-page: 685 year: 2019 ident: 1677_CR29 publication-title: Discrete Contin. Dyn. Syst. Ser. S. doi: 10.3934/dcdss.2019043 – volume: 57 start-page: 549 issue: 5–7 year: 2007 ident: 1677_CR7 publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2006.07.007 – ident: 1677_CR4 doi: 10.1017/CBO9780511626340 – volume: 22 start-page: 419 issue: 4 year: 1981 ident: 1677_CR26 publication-title: The ANZIAM Journal doi: 10.1017/S0334270000002769 – volume: 420 year: 2022 ident: 1677_CR28 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2021.126870 – volume-title: Linear integral equations year: 1989 ident: 1677_CR13 doi: 10.1007/978-3-642-97146-4 – volume: 234 start-page: 2848 issue: 9 year: 2010 ident: 1677_CR17 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2010.01.033 – volume: 19 start-page: 248 issue: 3 year: 1972 ident: 1677_CR3 publication-title: Numer. Math. doi: 10.1007/BF01404695 – volume: 43 start-page: 175 year: 2013 ident: 1677_CR18 publication-title: J. Appl. Math. Comput. doi: 10.1007/s12190-013-0658-0 – volume: 46 start-page: 1799 issue: 4 year: 2008 ident: 1677_CR27 publication-title: SIAM J. Numer. Anal. doi: 10.1137/070693308 – volume: 349 start-page: 314 year: 2019 ident: 1677_CR30 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2018.12.035 – volume: 13 start-page: 463 issue: 3 year: 1994 ident: 1677_CR20 publication-title: Zeitschrift für Analysis und ihre Anwendungen doi: 10.4171/zaa/501 – volume: 36 start-page: 207 issue: 153 year: 1981 ident: 1677_CR25 publication-title: Math. Comput. doi: 10.2307/2007737 – volume: 150 start-page: 41 issue: 1 year: 1970 ident: 1677_CR24 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1970-0410210-0 – volume: 73 start-page: 271 year: 2004 ident: 1677_CR22 publication-title: Computing doi: 10.1007/s00607-004-0088-9 – volume: 92 start-page: 2045 year: 2023 ident: 1677_CR10 publication-title: Numerical Algorithms doi: 10.1007/s11075-022-01376-x – ident: 1677_CR1 doi: 10.1201/9781420035827 – volume: 23 start-page: 1545 issue: 8 year: 1955 ident: 1677_CR5 publication-title: J. Chem. Phys. doi: 10.1063/1.1742352 – volume: 62 start-page: 739 issue: 206 year: 1994 ident: 1677_CR12 publication-title: Math. Comput. doi: 10.1090/S0025-5718-1994-1218345-X – volume: 13 start-page: 660 year: 1990 ident: 1677_CR11 publication-title: Integr. Eqn. Oper. Theory doi: 10.1007/BF01732317 – volume: 346 start-page: 224 year: 2019 ident: 1677_CR19 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2018.07.010 – volume: 349 start-page: 114 year: 2019 ident: 1677_CR15 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2018.09.032 |
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| SubjectTerms | Algebra Algorithms Comparative studies Computer Science Exact solutions Fredholm equations Galerkin method Integral equations Mathematical analysis Methods Numeric Computing Numerical Analysis Operators (mathematics) Original Paper Polynomials Regularity Smoothing Theory of Computation Transformations (mathematics) Weighting functions |
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| Title | A new approach of shifted Jacobi spectral Galerkin methods (SJSGM) for weakly singular Fredholm integral equation with non-smooth solution |
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