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

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...

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Published inJournal of computational mathematics Vol. 31; no. 1; pp. 47 - 56
Main Authors Chen, Yanping, Li, Xianjuan, Tang, Tao
Format Journal Article
LanguageEnglish
Published Chinese Academy of Mathematices and System Sciences (AMSS) Chinese Academy of Sciences 2013
Subjects
JACOBI
Volterra积分方程
光滑解
弱奇性
注记
积分方程组
配置方法
频谱
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Summary: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.
Bibliography: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.
Volterra integral equations, Convergence analysis, Spectral-collocation meth-ods.
11-2126/O1
ISSN:0254-9409
1991-7139
DOI:10.4208/jcm.1208-m3497