Research Reports from the Department of Operations
Document Type
Report
Publication Date
12-1-1961
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.
Keywords
Operations research, Differential equations, Engineering mathematics, Decomposition method--Mathematical models, Computational complexity, Problem solving, Mathematical optimization, Systems engineering, Numerical analysis, Computer simulation
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 16
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Chase, Hamilton A. and Sengupta, S. Sankar, "The Decomposition Principle in Engineering Problems: Towards a Multi-Level Concept of Problem Solving" (1961). Research Reports from the Department of Operations. 129.
https://commons.case.edu/wsom-ops-reports/129