The collocation method for the solution of boundary integral equations

Abstract

This article is devoted to investigating the approximate solutions to a class of boundary integral equations over a closed, bounded and smooth surface found via the collocation method. This article provides sufficient conditions for the convergence of this method in the space of continuous functions.

Keywords:

• boundary integral equation
• collocation method
• boundary value problem
• Helmholtz's equation

AMS Subject Classifications::

• 45E05
• 31B10

Acknowledgements

The authors would like to express sincere thanks to the referees for their useful comments and discussions. The authors also thank the American Journal Experts for their English language corrections.