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Problem with finite diffence method

  1. Mar 27, 2007 #1
    I have been trying to solve this problem for hours and hours but derivative boundary condition makes the it very hard. can anybody help me about nonlineer eq. solution with finite difference??

    question is:

    u'' + 3*u^2 *( 1 / (sin^2(x)) =2.5
    BCs:

    u'(1)=0.95
    u(2)=0.83
    h=0.25
    (radian for sin function)
     
  2. jcsd
  3. Mar 27, 2007 #2

    HallsofIvy

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    Exactly how are you applying "finite difference"? Are you assuming a linear solution overe each interval?
     
    Last edited: Mar 27, 2007
  4. Mar 28, 2007 #3

    arildno

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    As for the boundary condition, since it involves a derivative, you should regard it the actual left boundary as an interior point.
    Thus, introduce a fictitious boundary point [itex]x_{0}=1-h[/tex]
    and you have n+1 points [itex]x_{0}, x_{1}=1,\cdots{x}_{n}=2[/tex]

    The differential equation should be satisfied at all interior points, so that you have n+1 non-linear equations like this:
    [tex]\frac{u_{2}-u_{0}}{2h}=0.95, u_{n}=0.83[/tex]
    and:
    [tex]\frac{u_{i+1}-2u_{i}+u_{i-1}}{h^{2}}+3u_{i}^{2}\frac{1}{\sin^{2}(x_{i})}=2.5, i=1,\cdots{n-1}[/tex]

    Now, you are ready to see how to implement a loop structure to actually solve this system approximately..
     
    Last edited: Mar 28, 2007
  5. Mar 28, 2007 #4
    thanks for your attention
     
  6. Mar 28, 2007 #5

    arildno

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    Have you decided upon a strategy to take care of the non-linearity?
     
  7. Mar 29, 2007 #6
    yes newton method
     
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