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A Note on Jacobi Spectral-Collocation Methods for Weakly Singular Volterra Integral Equations with Smooth Solutions

A Note on Jacobi Spectral-Collocation Methods for Weakly Singular Volterra Integral Equations with Smooth Solutions
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Year:    2013

Journal of Computational Mathematics, Vol. 31 (2013), Iss. 1 : pp. 47–56

Abstract

This work is concerned with spectral Jacobi-collocation methods for Volterra integral equations of the second kind with a weakly singular of the form $(t-s)^{-\alpha}$. When the underlying solutions are sufficiently smooth, the convergence analysis was carried out in [Chen & Tang, J. Comput. Appl. Math., 233 (2009), pp. 938-950]; due to technical reasons the results are restricted to $0<\mu<\frac{1}{2}$. In this work, we will improve the results to the general case $0<\mu<1$ and demonstrate that the numerical errors decay exponentially in the infinity and weighted norms when the smooth solution is involved.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1208-m3497

Journal of Computational Mathematics, Vol. 31 (2013), Iss. 1 : pp. 47–56

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Volterra integral equations Convergence analysis Spectral-collocation methods.

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