Piecewise Spectral Collocation Method for Second Order Volterra Integro-Differential Equations with Nonvanishing Delay  

作　　者：Zhenrong Chen Yanping Chen Yunqing Huang 

机构地区：[1]School of Mathematical Sciences,South China Normal University,Guangzhou,Guangdong 510631,China [2]School of Mathematics and Computational Science,Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Xiangtan University,Xiangtan,Hunan 411105,China

出　　处：《Advances in Applied Mathematics and Mechanics》2022年第6期1333-1356,共24页应用数学与力学进展（英文）

基　　金：the State Key Program of National Natural Science Foundation of China(No.11931003);National Natural Science Foundation of China(Nos.41974133,and 12126325);Postgraduate Scientific Research Innovation Project of Hunan Province(No.CX20200620);Postgraduate Scientific Research Innovation Project of Xiangtan University(No.XDCX2020B087).

摘　　要：In this paper,the piecewise spectral-collocation method is used to solve the second-order Volterra integral differential equation with nonvanishing delay.In this collocation method,the main discontinuity point of the solution of the equation is used to divide the partitions to overcome the disturbance of the numerical error convergence caused by the main discontinuity of the solution of the equation.Derivative approximation in the sense of integral is constructed in numerical format,and the convergence of the spectral collocation method in the sense of the L¥and L2 norm is proved by the Dirichlet formula.At the same time,the error convergence also meets the effect of spectral accuracy convergence.The numerical experimental results are given at the end also verify the correctness of the theoretically proven results.

关 键 词：Second-order Volterra type integro-differential equation delay function piecewise spectral-collocation method. 

分 类 号：O17[理学—数学]