A collocation method based on roots of Chebyshev polynomial for solving Volterra integral equations of the second kind

This paper mainly studies numerical solution to the Volterra integral equation of the second kind. By using the roots of Chebyshev polynomial as collocation points, a new collocation method is proposed to solve the Volterra integral equation of the second kind. The proposed method firstly interpolates the product of the kernel function and the unknown solution at the roots of Chebyshev polynomial. Then, the Volterra integral equation is transformed into a system of linear algebra equations by properties of Chebyshev polynomials. Finally, the numerical solution of the Volterra integral equation is obtained by the Chebyshev polynomial interpolation. In addition, the error estimates of the proposed method are provided in a semi-posteriori sense; and numerical examples are given to show effectiveness of the proposed method. & COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

This study mainly focuses on the numerical solution to the second kind of Volterra integral equation. A new collocation method is proposed using the roots of Chebyshev polynomial as collocation points. The method interpolates the product of the kernel function and the unknown solution at the roots of Chebyshev polynomial, and transforms the Volterra integral equation into a system of linear algebra equations. The numerical solution is obtained by the Chebyshev polynomial interpolation and the effectiveness is demonstrated through numerical examples.