  This paper considers efficient spectral solutions for weakly singular
nonlocal diffusion equations with Dirichlet-type volume constraints. The
equation we consider contains an integral operator that typically has a
singularity at the midpoint of the integral domain, and the approximation of
the integral operator is one of the essential difficulties in solving nonlocal
equations. To overcome this problem, two-sided Jacobi spectral quadrature rules
are proposed to develop a Jacobi spectral collocation method for nonlocal
diffusion equations. A rigorous convergence analysis of the proposed method
with the $L^\infty$ norm is presented, and we further prove that the Jacobi
collocation solution converges to its corresponding local limit as nonlocal
interactions vanish. Numerical examples are given to verify the theoretical
results.
