Analytic solution with a priori error bounds for a class of mixed coupled partial differential equations

In this paper, the existence of a sequence of stable solutions Xn of the parametric matrix equation Z2 + AZ − n2B = 0 so that {Xn/n} converges to a stable matrix is studied. The result is used for solving mixed problems related to the coupled second-order partial differential system utt + Auxx + But = 0.