• 论文 •

### Volterra型积分方程的Galerkin Legendre Jacobi数值积分法

1. 1. 桂林电子科技大学, 数学与计算科学学院, 广西高校数据分析与计算重点实验室, 广西自动检测技术与仪器重点实验室, 桂林 541004;
2. 桂林电子科技大学, 广西应用数学中心, 桂林 541004
• 收稿日期:2021-12-29 发布日期:2023-03-16
• 通讯作者: 覃永辉,yonghui1676@163.com;yonghui@csrc.ac.cn.
• 基金资助:
国家自然科学基金（12161025，61963011，11961012，11961010）；广西自动检测技术与仪器重点实验室基金（YQ22106）；桂林电子科技大学研究生教育创新计划（2020YCXS086）资助.

Fan Youkang, Lu Rongwei, Qin Yonghui. GALERKIN LEGENDRE JACOBI NUMERICAL INTEGRAL FOR VOLTERRA INTEGRAL EQUATIONS[J]. Journal on Numerica Methods and Computer Applications, 2023, 44(1): 81-94.

### GALERKIN LEGENDRE JACOBI NUMERICAL INTEGRAL FOR VOLTERRA INTEGRAL EQUATIONS

Fan Youkang1, Lu Rongwei2, Qin Yonghui1,2

1. 1. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China;
2. Center for Applied Mathematics of Guangxi(GUET), Guilin 541004, China
• Received:2021-12-29 Published:2023-03-16

Galerkin Legendre Jacobi numerical integration method is investigated for the Volterratype integral equations. First, the integral term of the equation is approximated by using the Jacobi Galerkin numerical integral method, and an equivalent equation is obtained. Second, the Legendre Galerkin equation is developed for this equivalent model, and the integral term is calculated by Chebyshev interpolation. Then, our method is also extended to solve the nonlinear Volterra integral equations. Finally, by using the above method, we give a two-level multi-interval scheme for the Volterra integral equation with discontinuity. In addition, we also apply our scheme to solve the third class of Volterra integral equations. Some numerical examples are given to test the high-order accuracy and the effectiveness of the proposed method.

MR(2010)主题分类:

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