Frontiers of Mathematics in China

, Volume 14, Issue 2, pp 435–448

# Spectral method for multidimensional Volterra integral equation with regular kernel

• Yunxia Wei
• Yanping Chen
• Xiulian Shi
• Yuanyuan Zhang
Research Article

## Abstract

This paper is concerned with obtaining an approximate solution for a linear multidimensional Volterra integral equation with a regular kernel. We choose the Gauss points associated with the multidimensional Jacobi weight function $$\omega(x) = \prod{_{i=1}^d}(1 - x_i)^\alpha(1 + x_i)^\beta, -1 <\alpha,\beta < \frac{1}{d} - \frac{1}{2}$$ (d denotes the space dimensions) as the collocation points. We demonstrate that the errors of approximate solution decay exponentially. Numerical results are presented to demonstrate the effectiveness of the Jacobi spectral collocation method.

## Keywords

Multidimensional Volterra integral equation Jacobi collocation discretization multidimensional Gauss quadrature formula

## MSC

65R20 45J05 65N12

## Notes

### Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11671157, 11826212).

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## Authors and Affiliations

• Yunxia Wei
• 1
• Yanping Chen
• 2
Email author
• Xiulian Shi
• 3
• Yuanyuan Zhang
• 4
1. 1.Zhejiang University of Water Resources and Electric PowerHangzhouChina
2. 2.School of Mathematical SciencesSouth China Normal UniversityGuangzhouChina
3. 3.School of Mathematics and StatisticsZhaoqing UniversityZhaoqingChina
4. 4.Department of Mathematics and Information ScienceYantai UniversityYantaiChina