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Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind |
Xianjuan LI1, Tao TANG2( ) |
1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China; 2. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China |
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Abstract This work is to analyze a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel ?(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.
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Keywords
Jacobi spectral collocation method
Abel-Volterra integral equation
convergence analysis
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Corresponding Author(s):
TANG Tao,Email:ttang@math.hkbu.edu.hk
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Issue Date: 01 February 2012
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