Solving Poisson equations by boundary knot method

The boundary knot method (BKM) is a recent meshfree boundary-type radial basis function (RBF) collocation technique. Compared with the method of fundamental solution, the BKM uses the nonsingular general solution instead of the singular fundamental solution to evaluate the homogeneous solution, while as such the dual reciprocity method (DRM) is still employed to approximate the particular solution. However, it is noted that the nonsingular general solution of Laplace equation is a constant, the BKM can not thus directly applied to it. This paper is an extension of reference [1], where a simple BKM scheme was presented for solving Laplace equations. The scheme opens the door to use the BKM for general linear and nonlinear problems.