For the numerical solution of Volterra integral equations of the second kind whose integrands have diagonal and endpoint algebraic singularities, we investigate in this paper, a fast modified collocation method based on the zeros of the Jacobi polynomials in appropriate weighted spaces. The iterated version of the standard collocation method is also defined. The proposed methods are shown to converge faster than the collocation scheme, and the Sloan iteration can be applied to the modified collocation solution to make it even more accurate. This research seems to be the first to explore superconvergent approaches for solving integral equations of this type. Some numerical tests are presented to show the effectiveness of the suggested methods.(c) 2023 Elsevier B.V. All rights reserved.
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Univ Lyon, Inst Camille Jordan, UMR5208, 23 Rue Dr Paul Michelon, F-42023 St Etienne 2, FranceUniv Lyon, Inst Camille Jordan, UMR5208, 23 Rue Dr Paul Michelon, F-42023 St Etienne 2, France
Grammont, Laurence
Kulkarni, Rekha P.
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Indian Inst Technol, Dept Math, Mumbai 400076, Maharashtra, IndiaUniv Lyon, Inst Camille Jordan, UMR5208, 23 Rue Dr Paul Michelon, F-42023 St Etienne 2, France
Kulkarni, Rekha P.
Vasconcelos, Paulo B.
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Univ Porto, Fac Econ, CMUP, Rua Dr Roberto Frias, P-4200464 Porto, PortugalUniv Lyon, Inst Camille Jordan, UMR5208, 23 Rue Dr Paul Michelon, F-42023 St Etienne 2, France
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Harbin Inst Technol, Sch Sci, Shenzhen 518055, Peoples R ChinaHarbin Inst Technol, Sch Sci, Shenzhen 518055, Peoples R China
Liang, Hui
Brunner, Hermann
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Hong Kong Baptist Univ, Dept Math, Hong Kong, Peoples R China
Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, CanadaHarbin Inst Technol, Sch Sci, Shenzhen 518055, Peoples R China