  Nonlocal diffusion model provides an appropriate description of the diffusion
process of solute in the complex medium, which cannot be described properly by
classical theory of PDE. However, the operators in the nonlocal diffusion
models are nonlocal, so the resulting numerical methods generate dense or full
stiffness matrices. This imposes significant computational and memory challenge
for a nonlocal diffusion model.
  In this paper, we develop a spectral collocation method for the nonlocal
diffusion model and provide a rigorous error analysis which theoretically
justifies the spectral rate of convergence provided that the kernel functions
and the source functions are sufficiently smooth. Compared to finite difference
methods and finite element methods, because of the high order convergence
rates, the numerical cost of spectral collocation methods will be greatly
decreased. Numerical results confirm the exponential rate of convergence.
