  This paper has made some significant advances in the boundary-only and
domain-type RBF techniques. The proposed boundary knot method (BKM) is
different from the standard boundary element method in a number of important
aspects. Namely, it is truly meshless, exponential convergence,
integration-free (of course, no singular integration), boundary-only for
general problems, and leads to symmetric matrix under certain conditions (able
to be extended to general cases after further modified). The BKM also avoids
the artificial boundary in the method of fundamental solution. An amazing
finding is that the BKM can formulate linear modeling equations for nonlinear
partial differential systems with linear boundary conditions. This merit makes
it circumvent all perplexing issues in the iteration solution of nonlinear
equations. On the other hand, by analogy with Green's second identity, we also
presents a general solution RBF (GSR) methodology to construct efficient RBFs
in the domain-type RBF collocation method and dual reciprocity method. The GSR
approach first establishes an explicit relationship between the BEM and RBF
itself on the ground of the potential theory. This paper also discusses some
essential issues relating to the RBF computing, which include time-space RBFs,
direct and indirect RBF schemes, finite RBF method, and the application of
multipole and wavelet to the RBF solution of the PDEs.
