A SPECTRAL METHOD FOR A WEAKLY SINGULAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATION WITH PANTOGRAPH DELAY  

作　　者：Weishan ZHENG Yanping CHEN 郑伟珊;陈艳萍(College of Mathematics and Statistics,Hanshan Normal University,Chaozhou 521041,China;School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China)

机构地区：[1]College of Mathematics and Statistics,Hanshan Normal University,Chaozhou 521041,China [2]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China

出　　处：《Acta Mathematica Scientia》2022年第1期387-402,共16页数学物理学报（B辑英文版）

基　　金：supported by the State Key Program of National Natural Science Foundation of China(11931003);the National Natural Science Foundation of China(41974133,11671157)。

摘　　要：In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transformation to change the equation into a new Volterra integral equation defined on the standard interval[-1,1],so that the Jacobi orthogonal polynomial theory can be applied conveniently.In order to obtain high order accuracy for the approximation,the integral term in the resulting equation is approximated by Jacobi spectral quadrature rules.In the end,we provide a rigorous error analysis for the proposed method.The spectral rate of convergence for the proposed method is established in both the L^(∞)-norm and the weighted L^(2)-norm.

关 键 词：Volterra integro-differential equation pantograph delay weakly singular kernel Jacobi-collocation spectral methods error analysis convergence analysis 

分 类 号：O175[理学—数学]