Frontiers of Mathematics in China >
Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind
Received date: 29 Oct 2010
Accepted date: 29 Jul 2011
Published date: 01 Feb 2012
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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.
Xianjuan LI , Tao TANG . Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind[J]. Frontiers of Mathematics in China, 2012 , 7(1) : 69 -84 . DOI: 10.1007/s11464-012-0170-0
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