  This paper made some significant advances in the dual reciprocity and
boundary-only 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, this
paper also presents a general solution RBF (GSR) methodology to construct
efficient RBFs in the dual reciprocity and domain-type RBF collocation methods.
The GSR approach first establishes an explicit relationship between the BEM and
RBF itself on the ground of the weighted residual principle. This paper also
discusses the RBF convergence and stability problems within the framework of
integral equation theory.
