Before revision:  Thus, stability conditions are established through meshgrid constraints, discrete maximum principles, and, overall, exploiting the concept of Invariant regions , as developed in the work of Chueh, Conway, Smoller, and particularly in the application of their theory to finite-difference methods in the work of Hoff.
After revision:  Thus, stability conditions are established using the concept of Invariant regions , as developed in the work of Chueh, Conway, Smoller, and particularly in the application of their theory to finite-difference methods in the work of Hoff.