  A study is presented on the convergence of the computation of coupled
advection-diffusion-reaction equations. In the computation, the equations with
different coefficients and even types are assigned in two subdomains, and
Schwarz iteration is made between the equations when marching from a time level
to the next one. The analysis starts with the linear systems resulting from the
full discretization of the equations by explicit schemes. Conditions for
convergence are derived, and its speedup and the effects of difference in the
equations are discussed. Then, it proceeds to an implicit scheme, and a
recursive expression for convergence speed is derived. An optimal interface
condition for the Schwarz iteration is obtained, and it leads to "perfect
convergence", that is, convergence within two times of iteration. Furthermore,
the methods and analyses are extended to the coupling of the viscous Burgers
equations. Numerical experiments indicate that the conclusions, such as the
"perfect convergence, " drawn in the linear situations may remain in the
Burgers equations' computation.
