TY - JOUR

T1 - Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind

AU - Li, Xianjuan

AU - TANG, Tao

N1 - Funding Information:
Acknowledgements This work was are supported by the FRG Grant of Hong Kong Baptist University and the RGC Grants provided by Research Grant Council of Hong Kong, China.

PY - 2012/2

Y1 - 2012/2

N2 - 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.

AB - 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.

KW - Abel-Volterra integral equation

KW - convergence analysis

KW - Jacobi spectral collocation method

UR - http://www.scopus.com/inward/record.url?scp=84855726247&partnerID=8YFLogxK

U2 - 10.1007/s11464-012-0170-0

DO - 10.1007/s11464-012-0170-0

M3 - Article

AN - SCOPUS:84855726247

SN - 1673-3452

VL - 7

SP - 69

EP - 84

JO - Frontiers of Mathematics in China

JF - Frontiers of Mathematics in China

IS - 1

ER -