  This work is motivated by the frequent occurrence of boundary value problems
with various boundary conditions in the modeling of some problems in
engineering and physical science. Here we propose a new technique to force the
positive definite kernels such as some radial basis functions to satisfy the
boundary conditions exactly. It can improve the applications of existing
methods based on positive definite kernels and radial basis functions
especially the pseudospectral radial basis function method for handling the
differential equations with more complicated boundary conditions. The proposed
method is applied to a singularly perturbed steady-state convection-diffusion
problem, two and three dimensional Poisson's equations with various boundary
conditions.
