Legendre Spectral Projection Methods for Hammerstein Integral Equations with Weakly Singular Kernel

International Journal of Applied and Computational Mathematics ◽

10.1007/s40819-018-0580-0 ◽

2018 ◽

Vol 4 (6) ◽

Cited By ~ 1

Author(s):

Bijaya Laxmi Panigrahi

Keyword(s):

Integral Equations ◽

Spectral Projection ◽

Projection Methods ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Hammerstein Integral Equations ◽

Weakly Singular

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Discrete Legendre Collocation Methods for Fredholm–Hammerstein Integral Equations with Weakly Singular Kernel

Mathematics and Computing - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-981-13-2095-8_25 ◽

2018 ◽

pp. 315-328

Author(s):

Bijaya Laxmi Panigrahi

Keyword(s):

Integral Equations ◽

Collocation Methods ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Hammerstein Integral Equations ◽

Weakly Singular

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Superconvergence results of Legendre spectral projection methods for weakly singular Fredholm–Hammerstein integral equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.09.032 ◽

2019 ◽

Vol 349 ◽

pp. 114-131 ◽

Cited By ~ 9

Author(s):

Moumita Mandal ◽

Gnaneshwar Nelakanti

Keyword(s):

Integral Equations ◽

Spectral Projection ◽

Projection Methods ◽

Hammerstein Integral Equations ◽

Weakly Singular ◽

Superconvergence Results

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Legendre spectral projection methods for weakly singular Hammerstein integral equations of mixed type

The Journal of Analysis ◽

10.1007/s41478-019-00175-3 ◽

2019 ◽

Vol 28 (2) ◽

pp. 387-413 ◽

Cited By ~ 1

Author(s):

Subhashree Patel ◽

Bijaya Laxmi Panigrahi

Keyword(s):

Integral Equations ◽

Mixed Type ◽

Spectral Projection ◽

Projection Methods ◽

Hammerstein Integral Equations ◽

Equations Of Mixed Type ◽

Weakly Singular

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Error analysis of Jacobi spectral collocation methods for Fredholm-Hammerstein integral equations with weakly singular kernel

International Journal of Computer Mathematics ◽

10.1080/00207160.2018.1515428 ◽

2018 ◽

Vol 96 (6) ◽

pp. 1230-1253 ◽

Cited By ~ 2

Author(s):

Bijaya Laxmi Panigrahi

Keyword(s):

Error Analysis ◽

Integral Equations ◽

Collocation Methods ◽

Singular Kernel ◽

Spectral Collocation ◽

Weakly Singular Kernel ◽

Hammerstein Integral Equations ◽

Weakly Singular ◽

Spectral Collocation Methods

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Convergence analysis of discrete legendre spectral projection methods for hammerstein integral equations of mixed type

Applied Mathematics and Computation ◽

10.1016/j.amc.2015.05.100 ◽

2015 ◽

Vol 265 ◽

pp. 574-601 ◽

Cited By ~ 3

Author(s):

Payel Das ◽

Gnaneshwar Nelakanti

Keyword(s):

Convergence Analysis ◽

Integral Equations ◽

Mixed Type ◽

Spectral Projection ◽

Projection Methods ◽

Hammerstein Integral Equations ◽

Equations Of Mixed Type

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New spectral element method for Volterra integral equations with weakly singular kernel

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2021.113902 ◽

2021 ◽

pp. 113902

Author(s):

Chao Zhang ◽

Zhipeng Liu ◽

Sheng Chen ◽

DongYa Tao

Keyword(s):

Integral Equations ◽

Spectral Element Method ◽

Spectral Element ◽

Volterra Integral Equations ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Weakly Singular ◽

Element Method

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Erratum to: Discrete Legendre spectral projection methods for Fredholm–Hammerstein integral equations [J. Comput. Appl. Math. 278 (2015) 293–305]

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2015.08.005 ◽

2016 ◽

Vol 292 ◽

pp. 634-636

Author(s):

Payel Das ◽

Gnaneshwar Nelakanti ◽

Guangqing Long

Keyword(s):

Integral Equations ◽

Spectral Projection ◽

Projection Methods ◽

Hammerstein Integral Equations ◽

Appl Math

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A hybrid spectral element method for Volterra integral equations with weakly singular kernel

Scientia Sinica Mathematica ◽

10.1360/n012015-00207 ◽

2016 ◽

Keyword(s):

Integral Equations ◽

Spectral Element Method ◽

Spectral Element ◽

Volterra Integral Equations ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Weakly Singular ◽

Element Method

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The Jacobi Collocation Method for a Class of Nonlinear Volterra Integral Equations with Weakly Singular Kernel

Journal of Scientific Computing ◽

10.1007/s10915-016-0213-x ◽

2016 ◽

Vol 69 (2) ◽

pp. 673-695 ◽

Cited By ~ 5

Author(s):

Sonia Seyed Allaei ◽

Teresa Diogo ◽

Magda Rebelo

Keyword(s):

Integral Equations ◽

Collocation Method ◽

Volterra Integral Equations ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Weakly Singular ◽

Jacobi Collocation Method

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Convergence Analysis of the Spectral Method for Second-Kind Volterra Integral Equations with a Weakly Singular Kernel

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.263-266.3313 ◽

2012 ◽

Vol 263-266 ◽

pp. 3313-3316

Author(s):

Yiao Yong Zhang ◽

Hua Feng Wu

Keyword(s):

Integral Equations ◽

Source Function ◽

Volterra Integral Equations ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Weakly Singular ◽

L2 Norm ◽

Spectral Galerkin Method ◽

Rigorous Error ◽

Theoretical Results

The Legendre spectral Galerkin method for Volterra integral equations of the second kind with a weakly singular kernel is proposed in this paper. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors (in the L2 -norm and the L∞ -norm ) will decay exponentially provided that the source function is sufficiently smooth. Numerical examples are given to illustrate the theoretical results.

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