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 - Journal 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 -