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Nonlinear System of Equations Newton-Raphson and SOR Sucessive Over Relaxatiom

  1. Oct 29, 2009 #1
    1. The problem statement, all variables and given/known data
    3X1 - COS(X2*X3) – 0.5 = 0
    X1^2 - 81*(X2 + 0.1)^2 + SIN(X3) + 1.06 = 0
    EXP(-X1*X2) + 20*X3 + (10pi – 3)/3 = 0


    2. Relevant equations
    Newton Raphsom and Gauss Sceidal with relaxation term


    3. The attempt at a solution
    I've already solved the above system using Newton Raphsom and got an output of x=[0.5000, 0.0285,-0.5229] using various initial guesses. So far I've only been able to find one solution with my guesses with my Matlab code.

    I need some help understanding the method of solving this with SOR. My understanding and approach so far is to use the Newtom Raphsom method to linearize the system. Thus this will generate the delta x (the change in x). From there I can use SOR and input the value found from Newton and iterate until my error is maybe less than 10^-5.

    I just can't get it to converge to the answer that I want. One term in x seems to keep increasing and eventually blows up. Is my approach correct?
     
  2. jcsd
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