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Abstract:
In this paper, we discuss the superconvergence of the "interpolated" collocation solutions for weakly singular Volterra integral equations of the second kind. Based on the collocation solution u(h), two different interpolation postprocessing approximations of higher accuracy: I-2h(2m-1) u(h) based on the collocation points and I(2h)(m)u(h) based on the least square scheme are constructed, whose convergence order are the same as that of the iterated collocation solution. Such interpolation postprocessing methods are much simpler in computation. We further apply this interpolation postprocessing technique to hybrid collocation solutions and similar results are obtained. Numerical experiments are shown to demonstrate the efficiency of the interpolation postprocessing methods.
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Source :
COMPUTATIONAL & APPLIED MATHEMATICS
ISSN: 2238-3603
Year: 2021
Issue: 3
Volume: 40
2 . 6 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
ESI HC Threshold:31
JCR Journal Grade:1
Cited Count:
WoS CC Cited Count: 14
SCOPUS Cited Count: 14
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 8
Affiliated Colleges: