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Math Help - Eulers method fo dif eq..

  1. #1
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    Eulers method fo dif eq..

    In this example I need to implement Euler's method and produce a numerical solution

    so I have

    y'=y^2-2xy+1+x^2 which satisfies y(0)=-1;

    integrate over domain 0<x<5
    Last edited by reivera; March 7th 2008 at 04:12 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by reivera View Post
    In this example I need to implement Euler's method and produce a numerical solution

    so I have

    y'=y^2-2xy+1+x^2 which satisfies y(0)=-1;

    integrate over domain 0<x<5
    With Eulers method we write:

    y(x+h)=y(x)+h y'(x).

    Now we have y(0)=-1, so for example lets put h=0.2, then we have:

    Code:
       x      y(x)    y'(x)  y(x+h)
     0.0000 -1.0000  2.0000  0.4000 
     0.2000  0.4000  1.0400  0.4080 
     0.4000  0.4080  1.0001  0.6000 
     0.6000  0.6000  1.0000  0.8000 
     0.8000  0.8000  1.0000  1.0000 
     1.0000  1.0000  1.0000  1.2000 
     1.2000  1.2000  1.0000  1.4000 
     1.4000  1.4000  1.0000  1.6000 
     1.6000  1.6000  1.0000  1.8000 
     1.8000  1.8000  1.0000  2.0000 
     2.0000  2.0000  1.0000  2.2000 
     2.2000  2.2000  1.0000  2.4000 
     2.4000  2.4000  1.0000  2.6000 
     2.6000  2.6000  1.0000  2.8000 
     2.8000  2.8000  1.0000  3.0000 
     3.0000  3.0000  1.0000  3.2000 
     3.2000  3.2000  1.0000  3.4000 
     3.4000  3.4000  1.0000  3.6000 
     3.6000  3.6000  1.0000  3.8000 
     3.8000  3.8000  1.0000  4.0000 
     4.0000  4.0000  1.0000  4.2000 
     4.2000  4.2000  1.0000  4.4000 
     4.4000  4.4000  1.0000  4.6000 
     4.6000  4.6000  1.0000  4.8000 
     4.8000  4.8000  1.0000  5.0000 
     5.0000  5.0000  1.0000  5.2000
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