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Chakraborty, Samiran, Agrawal, Shivam Kumar, Nelakanti, Gnaneshwar (2025) Spectral approximated superconvergent methods for system of nonlinear Volterra Hammerstein integral equations. Chaos, Solitons & Fractals, 192. doi:10.1016/j.chaos.2025.116008

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Reference TypeJournal (article/letter/editorial)
TitleSpectral approximated superconvergent methods for system of nonlinear Volterra Hammerstein integral equations
JournalChaos, Solitons & Fractals
AuthorsChakraborty, SamiranAuthor
Agrawal, Shivam KumarAuthor
Nelakanti, GnaneshwarAuthor
Year2025 (March)Volume192
PublisherElsevier BV
DOIdoi:10.1016/j.chaos.2025.116008Search in ResearchGate
Generate Citation Formats
Mindat Ref. ID17993485Long-form Identifiermindat:1:5:17993485:8
GUID0
Full ReferenceChakraborty, Samiran, Agrawal, Shivam Kumar, Nelakanti, Gnaneshwar (2025) Spectral approximated superconvergent methods for system of nonlinear Volterra Hammerstein integral equations. Chaos, Solitons & Fractals, 192. doi:10.1016/j.chaos.2025.116008
Plain TextChakraborty, Samiran, Agrawal, Shivam Kumar, Nelakanti, Gnaneshwar (2025) Spectral approximated superconvergent methods for system of nonlinear Volterra Hammerstein integral equations. Chaos, Solitons & Fractals, 192. doi:10.1016/j.chaos.2025.116008
In(2025) Chaos, Solitons & Fractals Vol. 192. Elsevier BV

References Listed

These are the references the publisher has listed as being connected to the article. Please check the article itself for the full list of references which may differ. Not all references are currently linkable within the Digital Library.

Volterra (1927) Fluttuazioni del numero d’indinvidui in specie animali conviventi
Babolian, E., Mordad, M. (2011) A numerical method for solving systems of linear and nonlinear integral equations of the second kind by hat basis functions. Computers & Mathematics with Applications, 62. 187-198 doi:10.1016/j.camwa.2011.04.066
Biazar, J., Ghazvini, H. (2009) He’s homotopy perturbation method for solving systems of Volterra integral equations of the second kind. Chaos, Solitons & Fractals, 39. 770-777 doi:10.1016/j.chaos.2007.01.108
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Maleknejad (2004) Appl Math Comput Using Runge–Kutta method for numerical solution of the system of Volterra integral equation 149, 399
Wazwaz (2011)
Marzban, Hamid Reza, Nezami, Atiyeh (2022) Analysis of nonlinear fractional optimal control systems described by delay Volterra–Fredholm integral equations via a new spectral collocation method. Chaos, Solitons & Fractals, 162. 112499 doi:10.1016/j.chaos.2022.112499
Golbabai, A., Keramati, B. (2008) Easy computational approach to solution of system of linear Fredholm integral equations. Chaos, Solitons & Fractals, 38. 568-574 doi:10.1016/j.chaos.2007.01.036
Blom, J. G., Brunner, H. (1987) The Numerical Solution of Nonlinear Volterra Integral Equations of the Second Kind by Collocation and Iterated Collocation Methods. SIAM Journal on Scientific and Statistical Computing, 8 (5) 806-830 doi:10.1137/0908068
Brunner, Hermann (1985) The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes. Mathematics of Computation, 45 (172) 417-437 doi:10.1090/s0025-5718-1985-0804933-3
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Brunner, Hermann, Pedas, Arvet, Vainikko, Gennadi (1999) The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations. Mathematics of Computation, 68 (227) 1079-1095 doi:10.1090/s0025-5718-99-01073-x
Not Yet Imported: SIAM Journal on Numerical Analysis - journal-article : 10.1137/0721070

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Brunner (2017)
Not Yet Imported: Communications in Nonlinear Science and Numerical Simulation - journal-article : 10.1016/j.cnsns.2023.107783

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Chakraborty (2023) J Comput Appl Math Superconvergent multi-Galerkin method for nonlinear fredholm-Hammerstein integral equations 426
Chakraborty (2023) Appl Math Comput Superconvergence of system of Volterra integral equations by spectral approximation method 441
Kant (2020) Int J Comput Math Error analysis of Jacobi–Galerkin method for solving weakly singular Volterra–Hammerstein integral equations , 1
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Lubich, Ch. (1983) Runge-Kutta theory for Volterra and Abel integral equations of the second kind. Mathematics of Computation, 41 (163) 87-102 doi:10.1090/s0025-5718-1983-0701626-6
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Not Yet Imported: IMA Journal of Numerical Analysis - journal-article : 10.1093/imanum/7.3.313

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Kumar, Sunil, Sloan, Ian H. (1987) A new collocation-type method for Hammerstein integral equations. Mathematics of Computation, 48 (178) 585 doi:10.1090/s0025-5718-1987-0878692-4
Allaei, Sonia Seyed, Diogo, Teresa, Rebelo, Magda (2016) The Jacobi Collocation Method for a Class of Nonlinear Volterra Integral Equations with Weakly Singular Kernel. Journal of Scientific Computing, 69. 673-695 doi:10.1007/s10915-016-0213-x
Not Yet Imported: - journal-article : 10.1007/s40314-017-0563-5

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Mandal (2017) Commun Comput Inf Sci Superconvergence results for Volterra-Urysohn integral equations of second kind 655, 358
Not Yet Imported: Applied Mathematical Modelling - journal-article : 10.1016/j.apm.2014.12.046

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Not Yet Imported: - journal-article : 10.1515/jnma-2014-0014

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Vainikko, G.M. (1967) Galerkin's perturbation method and the general theory of approximate methods for non-linear equations. USSR Computational Mathematics and Mathematical Physics, 7 (4). 1-41 doi:10.1016/0041-5553(67)90140-1
Cheney (1966)
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See Also

These are possibly similar items as determined by title/reference text matching only.

Chakraborty, Samiran, Agrawal, Shivam Kumar, Nelakanti, Gnaneshwar (2025) Spectral approximated superconvergent method for nonlinear Volterra Hammerstein integral equations with weakly singular kernels. Journal of Computational and Applied Mathematics, 467. doi:10.1016/j.cam.2025.116601
Chakraborty, Samiran, Kumar Agrawal, Shivam, Nelakanti, Gnaneshwar (2025) Superconvergent spectral projection and multi-projection methods for nonlinear Fredholm integral equations. International Journal of Computer Mathematics, 102 (2). doi:10.1080/00207160.2024.2415697
Chakraborty, Samiran, Agrawal, Shivam Kumar, Nelakanti, Gnaneshwar (2023) Superconvergent multi-Galerkin method for nonlinear Fredholm–Hammerstein integral equations. Journal of Computational and Applied Mathematics, 426. 115092 doi:10.1016/j.cam.2023.115092
Chakraborty, Samiran, Nelakanti, Gnaneshwar (2025) Jacobi spectral methods for system of nonlinear Volterra Urysohn integral equations. Journal of Mathematical Analysis and Applications, 543 (1). doi:10.1016/j.jmaa.2024.128956
Chakraborty, Samiran, Kant, Kapil, Nelakanti, Gnaneshwar (2022) Error analysis of reiterated projection methods for Hammerstein integral equations. International Journal of Computer Mathematics, 99 (10) 2001-2017 doi:10.1080/00207160.2022.2028778
Mandal, Moumita, Kant, Kapil, Nelakanti, Gnaneshwar (2021) Discrete Legendre spectral methods for Hammerstein type weakly singular nonlinear Fredholm integral equations. International Journal of Computer Mathematics, 98 (11) 2251-2267 doi:10.1080/00207160.2021.1891225
Mandal, Moumita, Nelakanti, Gnaneshwar (2017) Superconvergence of Legendre spectral projection methods for Fredholm–Hammerstein integral equations. Journal of Computational and Applied Mathematics, 319. 423-439 doi:10.1016/j.cam.2017.01.027
Das, Payel, Nelakanti, Gnaneshwar, Long, Guangqing (2015) Discrete Legendre spectral projection methods for Fredholm–Hammerstein integral equations. Journal of Computational and Applied Mathematics, 278. 293-305 doi:10.1016/j.cam.2014.10.012
Bildik, Necdet, Inc, Mustafa (2007) Modified decomposition method for nonlinear Volterra–Fredholm integral equations. Chaos, Solitons & Fractals, 33. 308-313 doi:10.1016/j.chaos.2005.12.058
Mandal, Moumita, Nelakanti, Gnaneshwar (2019) Superconvergence results of Legendre spectral projection methods for weakly singular Fredholm–Hammerstein integral equations. Journal of Computational and Applied Mathematics, 349. 114-131 doi:10.1016/j.cam.2018.09.032
Marzban, Hamid Reza, Nezami, Atiyeh (2022) Analysis of nonlinear fractional optimal control systems described by delay Volterra–Fredholm integral equations via a new spectral collocation method. Chaos, Solitons & Fractals, 162. 112499 doi:10.1016/j.chaos.2022.112499
 
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