• 论文 •

### 非线性第二类Volterra积分方程的Chebyshev谱配置法

1. 1 广东金融学院金融数学与统计学院, 广州 5105211;
2 广东金融学院保险学院, 广州 510521
• 收稿日期:2018-11-05 出版日期:2020-11-15 发布日期:2020-11-15
• 基金资助:

广东省自然科学基金项目（2017A030310636，2018A030313236），广东省高性能计算学会开放基金项目（2017060104），中山大学广东省计算科学重点实验室开放基金项目（2016001），广东高校省级重点平台和重大科研项目（2017KTSCX131），广东省教育厅科研项目（2017KTSCX130）资助.

Gu Zhendong, Sun Liying. CHEBYSHEV SPECTRAL COLLOCATION METHOD FOR NONLINEAR VOLTERRA INTEGRAL EQUATIONS OF THE SECOND KIND[J]. Mathematica Numerica Sinica, 2020, 42(4): 445-456.

### CHEBYSHEV SPECTRAL COLLOCATION METHOD FOR NONLINEAR VOLTERRA INTEGRAL EQUATIONS OF THE SECOND KIND

Gu Zhendong1, Sun Liying2

1. 1 School of Financial Mathematics&Statistics, Guangdong University of Finance, Guangzhou 510521, China;
2 School of Insurance, Guangdong University of Finance, Guangzhou 510521, China
• Received:2018-11-05 Online:2020-11-15 Published:2020-11-15

Base on related references, we investigate the Chebyshev spectral collocation method for nonlinear Volterra integral equations of the second kind. The main idea of the presented method is to approximate numerically the new equations which are tranformedfrom the nonlinear Volterra integral equations of the second kind. The collocation points are Chebyshev Gauss-Lobatto points of order N. The integral terms are approximated by Gauss quadrature formula of order N. The provided convergence analysis shows thatthe convergence rate of the numerical errors is N(1/2)-m provided that the given functions are m times continuous differentiable. This theoretical result is confirmed by the provided numerical experiments.

MR(2010)主题分类:

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