A mesh-free method for linear diffusion equations

A "mesh-free" and "time-free" numerical method, based on the method of fundamental solutions, the dual reciprocity method (DRM) for the modified Helmholtz operator, and the Laplace transform, has been developed to solve diffusion-type and diffusion-reaction problems. Our proposed method has achieved both excellent accuracy and efficiency, as illustrated by two numerical examples, in two dimensions and three dimensions. Another attractive feature of our proposed method is the easy implementation for the 3D problems.