Scholarly Commons @ Case Western Reserve University
Abstract
In a previous report it was shown that a large system of differential equations could be decomposed into smaller groups (called subproblems) such that the solutions of the subproblems converged to the solution of the original system. It was also shown that the decomposition was most effective when the original problem was decomposed along the boundaries of weakest interaction in terms of the Lipschitz constants. This last fact, however, is a desirable but not essential condition. The major purpose of the present report is to develop certain techniques which will facilitate the application of the decomposition principle as stated in Tech Memo No. 14. The techniques fall into two categories: (a) those that help indicate how the grouping may be done in a natural and efficient manner, and (b) those that lead to a prior simplification of the original problem before the variables are grouped. Techniques of the first category make use of what has been called directed graphs ; those of the second category concentrate on the various types of linearization
