The multi-projection method for weakly singular Fredholm integral equations of the second kind

Abstract

In this paper, we propose a multi-projection method and its re-iterated algorithm for solving weakly singular Fredholm integral equations of the second kind. We apply our methods to Petrov–Galerkin versions to establish excellent superconvergence results, and we illustrate our theoretical results with a numerical example.

Keywords:

• super-convergence rates
• multi-projection methods
• singularity preserving
• Petrov–Galerkin methods
• integral equations

2000 AMS Subject Classifications :

• 65R20
• 65J10

Acknowledgements

This work was supported in part by the China Postdoctoral Science Foundation under grant 2005037603 and the Guangxi Science Foundation of P.R. China under grant 0728044.