By Topic

Algorithms for solving nonlinear equation systems assist students to become better problem solvers

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
C. J. Egelhoff ; US Coast Guards Acad., New London, CT, USA ; D. M. Blackketter ; J. L. Benson

In this paper, we present the distinguishing characteristics of "easy" and "hard" sets of equations and show the difference between simulation and design type problems. Easy equation sets have one unknown variable in each equation such that the equations can be solved sequentially. Hard equation sets have one critical unknown located in many (or all) of the equations in the set such that many (or all) of the equations must be solved simultaneously. We call these equations "coupled" and we teach students how they can analyze equation sets (based on the location of known and unknown variables) to "decouple" the equations and make the solution path easy. We describe the algorithm called the DeCoupler, which is used to identify variable interactions to determine the optimal decoupling variables. We also describe the SmartSwapper algorithm, which uses information from the DeCoupler to simplify the solution path and parametrically iterate to a solution. The algorithms are logic based rather than numerically focused. The algorithms have been implemented into an equation solving software program (SmartSolve2) to demonstrate their effectiveness compared to other commercial strategies. It has been shown that these algorithms can solve nonlinear simultaneous equations without the need for highly refined initial guesses. By teaching the concepts of these algorithms, students are assisted in becoming more effective problem solvers.

Published in:

Frontiers in Education Conference, 1999. FIE '99. 29th Annual  (Volume:1 )

Date of Conference:

10-13 Nov. 1999