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

doi:10.1007/s10473-022-0121-0

Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (1): 387-402.doi: 10.1007/s10473-022-0121-0

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

Weishan ZHENG¹, Yanping CHEN²

1. College of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China;
2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

Received:2020-05-27 Revised:2021-06-01 Online:2022-02-25 Published:2022-02-24
Contact: Yanping CHEN,E-mail:yanpingchen@scnu.edu.cn E-mail:yanpingchen@scnu.edu.cn
Supported by:
This work was supported by the State Key Program of National Natural Science Foundation of China (11931003) and the National Natural Science Foundation of China (41974133, 11671157).

Abstract

Abstract: 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 L²-norm.

Key words: Volterra integro-differential equation, pantograph delay, weakly singular kernel, Jacobi-collocation spectral methods, error analysis, convergence analysis

CLC Number:

65R20

Weishan ZHENG, Yanping CHEN. A SPECTRAL METHOD FOR A WEAKLY SINGULAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATION WITH PANTOGRAPH DELAY[J].Acta mathematica scientia,Series B, 2022, 42(1): 387-402.

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

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