  In this paper, we investigate ultraspherical spectral method for the
Ohta-Kawasaki (OK) and Nakazawa-Ohta (NO) models in the disk domain,
representing diblock and triblock copolymer systems, respectively. We employ
ultraspherical spectral discretization for spatial variables in the disk domain
and apply the second-order backward differentiation formula (BDF) method for
temporal discretization. To our best knowledge, this is the first study to
develop a numerical method for diblock and triblock copolymer systems with
long-range interactions in disk domains. We show the energy stability of the
numerical method in both semi-discrete and fully-discrete discretizations. In
our numerical experiments, we verify the second-order temporal convergence rate
and the energy stability of the proposed methods. Our numerical results show
that the coarsening dynamics in diblock copolymers lead to bubble assemblies
both inside and on the boundary of the disk. Additionally, in the triblock
copolymer system, we observe several novel pattern formations, including single
and double bubble assemblies in the unit disk. These findings are detailed
through extensive numerical experiments.
