Volume 60, pp. 446-470, 2024.

Error analysis of a Jacobi modified projection-type method for weakly singular Volterra-Hammerstein integral equations

Hamza Bouda, Chafik Allouch, Kapil Kant, and Zakaria El Allali

Abstract

The paper proposes polynomial-based projection-type and modified projection-type methods to solve weakly singular Volterra–Hammerstein integral equations of the second kind. Jacobi polynomials are used as basis functions. This type of equations often exhibits singular behavior at the left endpoint of the integration interval, and the exact solutions are typically nonsmooth. In the method under consideration, the independent variable is first transformed to provide a new integral equation with a smoother solution, allowing the Jacobi spectral method to be easily applied to the transformed equation and a full convergence analysis of the method to be performed. In different numerical tests, the effectiveness of the proposed approach is demonstrated.

Full Text (PDF) [599 KB], BibTeX

Key words

Volterra–Hammerstein integral equations, Jacobi polynomials, weakly singular kernels, orthogonal projection, interpolatory projection, superconvergence

AMS subject classifications

45B05, 45G10, 65R20

< Back