  We numerically solve two-dimensional heat diffusion problems by using a
simple variant of the meshfree local radial-basis function (RBF) collocation
method. The main idea is to include an additional set of sample nodes outside
the problem domain, similarly to the method of images in electrostatics, to
perform collocation on the domain boundaries. We can thereby take into account
the temperature profile as well as its gradients specified by boundary
conditions at the same time, which holds true even for a node where two or more
boundaries meet with different boundary conditions. We argue that the image
method is computationally efficient when combined with the local RBF
collocation method, whereas the addition of image nodes becomes very costly in
case of the global collocation. We apply our modified method to a benchmark
test of a boundary value problem, and find that this simple modification
reduces the maximum error from the analytic solution significantly. The
reduction is small for an initial value problem with simpler boundary
conditions. We observe increased numerical instability, which has to be
compensated for by a sufficient number of sample nodes and/or more careful
parameter choices for time integration.
