Civil and Environmental Engineering 2219A/B Study Guide - Final Guide: Nonlinear System, Antiderivative, Composite Application

• School: Western University
• Department: Civil and Environmental Engineering
• Course: Civil and Environmental Engineering 2219A/B
• Professor: Martha Dagnew

Document Summary

To solve systems of non-linear equations, we have to use iterative methods. Def: this approach combines gauss-seidel (linear systems) and fixed point iteration (roots) Steps involve rearranging the equations and solving each nonlinear system for one of the unknowns and update each unknown using information from the previous iteration. Note, there will be multiple approaches based upon how you manipulate the equations. Create a "g(x)" equation like we did for fixed-point iteration for every nonlinear equation in the system. Recall: for simple fixed-point iteration, the new function g(x) can be developed by rearranging the function ( ) = 0 so that x is on the left hand a. side of the equation. Create "options" equations a. i. e. from the equations in 2, rearrange in order to have them yield the unknowns x1 and/or x2, etc. Do this for all possibilities of the unknowns. Iterate based upon two of your options equations.