TY - JOUR
T1 - A note on Jacobi spectral-collocation methods for weakly singular Volterra integral equations with smooth solutions
AU - Chen, Yanping
AU - Li, Xianjuan
AU - TANG, Tao
N1 - This work is supported by National Science Foundation of China (11271145), Foundation for Talent Introduction of Guangdong Provincial University, Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2008), Specialized Research Fund for the Doctoral Program of Higher Education (20114407110009), and the Project of Department of Education of Guangdong Province (No. [2012] 290). The second author is supported by the Natural Science Foundation of Fujian Province, China (2012J01007) and Start-up fund of Fuzhou University (0460022456). The second and third author are supported by the FRG Grant of Hong Kong Baptist University and the RGC Grants provided by Research Grant Council of Hong Kong.
PY - 2013/1
Y1 - 2013/1
N2 - 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)-α. 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 < μ < 1/2 In this work, we will improve the results to the general case 0 < μ < 1 and demonstrate that the numerical errors decay exponentially in the infinity and weighted norms when the smooth solution is involved.
AB - 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)-α. 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 < μ < 1/2 In this work, we will improve the results to the general case 0 < μ < 1 and demonstrate that the numerical errors decay exponentially in the infinity and weighted norms when the smooth solution is involved.
KW - Convergence analysis
KW - Spectral-collocation methods
KW - Volterra integral equations
UR - http://www.scopus.com/inward/record.url?scp=84874971404&partnerID=8YFLogxK
U2 - 10.4208/jcm.1208-m3497
DO - 10.4208/jcm.1208-m3497
M3 - Journal article
AN - SCOPUS:84874971404
SN - 0254-9409
VL - 31
SP - 47
EP - 56
JO - Journal of Computational Mathematics
JF - Journal of Computational Mathematics
IS - 1
ER -