A NOTE ON JACOBI SPECTRAL-COLLOCATION METHODS FOR WEAKLY SINGULAR VOLTERRA INTEGRAL EQUATIONS WITH SMOOTH SOLUTIONS  

作　　者：Yanping Chen Xianjuan Li Tao Tang 

机构地区：[1]School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China [2]College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350108, China [3]Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

出　　处：《Journal of Computational Mathematics》2013年第1期47-56,共10页计算数学（英文）

基　　金：Acknowledgments. This work is supported by National Science Foundation of China （1127114 5）, 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 sup- ported 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.

摘　　要：This work is concerned with spectrM Jacobi-collocation methods for Volterra integral equations of the second kind with a weakly singular of the form （t - s）-a 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 1 In this work, we will improve the results to the the results are restricted to 0 〈 μ 〈 1/2. general case 0 〈 μ 〈 1 and demonstrate that the numericl errors decay exponentially in the infinity and weighted norms when the smooth solution is involved.This work is concerned with spectrM Jacobi-collocation methods for Volterra integral equations of the second kind with a weakly singular of the form （t - s）-a 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 1 In this work, we will improve the results to the the results are restricted to 0 〈 μ 〈 1/2. general case 0 〈 μ 〈 1 and demonstrate that the numericl errors decay exponentially in the infinity and weighted norms when the smooth solution is involved.

关 键 词：Volterra integral equations Convergence analysis Spectral-collocation meth-ods. 

分 类 号：O175.5[理学—数学] TB115[理学—基础数学]