  This paper is concerned with the two new boundary-type radial basis function
collocation schemes, boundary knot method (BKM) and boundary particle method
(BPM). The BKM is developed based on the dual reciprocity theorem, while the
BPM employs the multiple reciprocity technique. Unlike the method of
fundamental solution, the wto methods use the nonsingular general solutions
instead of singular fundamental solution to circumvent the controversial
artificial boundary outside physical domain. Compared with the boundary element
method, both the BKM and BPM are meshfree, superconvergent, meshfree,
integration free, symmetric, and mathematically simple collocation techniques
for general PDEs. In particular, the BPM does not require any inner nodes for
inhomogeneous problems. In this study, the accuracy and efficiency of the two
methods are numerically demonstrated to some 2D, 3D Helmholtz and
convection-diffusion problems under complicated geometries.
