  A few novel radial basis function (RBF) discretization schemes for partial
differential equations are developed in this study. For boundary-type methods,
we derive the indirect and direct symmetric boundary knot methods. Based on the
multiple reciprocity principle, the boundary particle method is introduced for
general inhomogeneous problems without using inner nodes. For domain-type
schemes, by using the Green integral we develop a novel Hermite RBF scheme
called the modified Kansa method, which significantly reduces calculation
errors at close-to-boundary nodes. To avoid Gibbs phenomenon, we present the
least square RBF collocation scheme. Finally, five types of the kernel RBF are
also briefly presented.
