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author:

Li, X. (Li, X..) [1] | Tang, T. (Tang, T..) [2]

Indexed by:

Scopus CSCD

Abstract:

This work is to analyze a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel φ(t, s) = (t - s) -μ. In an earlier work of Y. Chen and T. Tang [J. Comput. Appl. Math., 2009, 233: 938-950], the error analysis for this approach is carried out for 0 <μ<1/2 under the assumption that the underlying solution is smooth. It is noted that there is a technical problem to extend the result to the case of Abel-type, i. e., μ = 1/2. In this work, we will not only extend the convergence analysis by Chen and Tang to the Abel-type but also establish the error estimates under a more general regularity assumption on the exact solution. © 2012 Higher Education Press and Springer-Verlag Berlin Heidelberg.

Keyword:

Abel-Volterra integral equation; convergence analysis; Jacobi spectral collocation method

Community:

  • [ 1 ] [Li, X.]College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China
  • [ 2 ] [Tang, T.]Department of Mathematics, Hong Kong Baptist University, Hong Kong, China

Reprint 's Address:

  • [Tang, T.]Department of Mathematics, Hong Kong Baptist University, Hong Kong, China

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Source :

Frontiers of Mathematics in China

ISSN: 1673-3452

Year: 2012

Issue: 1

Volume: 7

Page: 69-84

0 . 3 2 3

JCR@2012

0 . 8 0 0

JCR@2023

JCR Journal Grade:4

CAS Journal Grade:4

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count: 60

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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