A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain

摘要

A recently discovered transform approach allows a large class of PDEs to be solved in terms of boundary and/or contour integrals. We introduce here a spectrally accurate numerical discretization of this approach for the case of Laplace's equation on a polygonal domain, and compare it against an also spectrally accurate implementation of the traditional boundary integral formulation. This journal is