Geodesic
Superconvergence of Hermite rule for third order hypersingular integrals on interval
Filomat, Tome 37 (2023) no. 29, p. 10065

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DOI

The boundary element method has been widely applied to a lot of practical problems,such as fluid mechanics and fracture mechanics. As one of the important topics in boundary element method, the numerical calculation of hypersingular integrals is of great importance. This article deals with the composite Hermite rule of the third order hypersingular integrals. Based on the error expansion, the superconvergence result of the composite Hermite formula is obtained. We show that the convergence rate is O(h 3) when the local coordinate of the singular point is τ = 0, which is one order higher than the global convergence. The accuracy of the result is verified by several numerical examples.
DOI : 10.2298/FIL2329065L
Classification : 65D30, 65D32
Keywords: Composite Hermite rule, Third order hypersingular integral, Superconvergence phenomenon, Special function, Error expansion 
Jin Li; Yu Sang; Xiaolei Zhang. Superconvergence of Hermite rule for third order hypersingular integrals on interval. Filomat, Tome 37 (2023) no. 29, p. 10065 . doi: 10.2298/FIL2329065L
@article{10_2298_FIL2329065L,
     author = {Jin Li and Yu Sang and Xiaolei Zhang},
     title = {Superconvergence of {Hermite} rule for third order hypersingular integrals on interval},
     journal = {Filomat},
     pages = {10065 },
     year = {2023},
     volume = {37},
     number = {29},
     doi = {10.2298/FIL2329065L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2329065L/}
}
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