The stable discrete numerical solution of strongly coupled mixed partial differential systems

This paper is concerned with the discrete numerical solution of coupled partial differential mixed problems with non-Dirichlet coupled boundary value conditions. By application of a discrete separation of variables method, the proposed numerical solution of the problem turns out to be the exact solution of certain coupled partial difference system, appearing from the discretization of the continuous partial differential system. Our approach avoids the iterative solution of algebraic systems which appears when one uses simple discretization methods. Existence, stability and the construction of solutions are considered.