A meshless like method for the approximate solution of integral equations over polygons

In this paper, a numerical scheme based on a Gauss-like cubature formula from Sammariva and Vianello (2007) [1] is introduced for approximate solution of integral equations over a polygonal domain with a piecewise straight lines boundary in R2. The proposed technique is a meshless like method with sufficient precision, which does not require any discretization of the polygon domain or any preprocessing such as mesh refinement. The error analysis of the method is provided and some numerical experiments are also presented to evaluate the performance of the proposed algorithm.