TY - JOUR
T1 - Spectral methods for weakly singular Volterra integral equations with smooth solutions
AU - Chen, Yanping
AU - TANG, Tao
N1 - Funding Information:
The authors are grateful to Mr. Xiang Xu of Fudan University for his assistance in the numerical work. The first author is supported by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2008), National Science Foundation of China, and the National Basic Research Program under the Grant 2005CB321703. The second author is supported by the FRG Grant of Hong Kong Baptist University and the RGC Grants provided by Research Grant Council of Hong Kong. His research is also supported in part by the Joint Research Fund for Hong Kong and Macau Young Scholars under the National Science Fund for Distinguished Young Scholars Scheme, National Natural Science Foundation of China.
PY - 2009/12/15
Y1 - 2009/12/15
N2 - We propose and analyze a spectral Jacobi-collocation approximation for the linear Volterra integral equations (VIEs) of the second kind with weakly singular kernels. In this work, we consider the case when the underlying solutions of the VIEs are sufficiently smooth. In this case, we provide a rigorous error analysis for the proposed method, which shows that the numerical errors decay exponentially in the infinity norm and weighted Sobolev space norms. Numerical results are presented to confirm the theoretical prediction of the exponential rate of convergence. Crown
AB - We propose and analyze a spectral Jacobi-collocation approximation for the linear Volterra integral equations (VIEs) of the second kind with weakly singular kernels. In this work, we consider the case when the underlying solutions of the VIEs are sufficiently smooth. In this case, we provide a rigorous error analysis for the proposed method, which shows that the numerical errors decay exponentially in the infinity norm and weighted Sobolev space norms. Numerical results are presented to confirm the theoretical prediction of the exponential rate of convergence. Crown
KW - Error analysis
KW - Smooth solutions
KW - Spectral methods
KW - Volterra integral equations
KW - Weakly singular kernels
UR - http://www.scopus.com/inward/record.url?scp=70349737556&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2009.08.057
DO - 10.1016/j.cam.2009.08.057
M3 - Journal article
AN - SCOPUS:70349737556
SN - 0377-0427
VL - 233
SP - 938
EP - 950
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 4
ER -