Radial basis function approximation in the dual reciprocity method (Q1339839)

The Poisson equation \(\Delta u= f\) is solved on a domain in the plane, and the method of solution is by a boundary integral equation. The source term \(f\) is taken into account by an approximation in terms of certain particular solutions. Specifically, an approximation \((*)\) \(f(P)\approx \sum_ j c_ j G(P,P_ j)\) is used, based on a collection of interpolation points \(P_ j\). The function \(G\) is such that explicit solutions of \(\Delta u= G\) are known. Computer experiments are made to estimate the condition number associated with \((*)\), and some pointwise errors are calculated.