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Function composition in finite differences

  1. Aug 26, 2011 #1
    Hi. Im trying to express the following in finite differences:

    [ tex ] \frac{d}{x}\left[ A(x)\frac{d\, u(x)}{x} \right] [ /tex ]

    If I take centered differences I get:

    [ tex ] \left{ \frac{d}{x}\left[ A(x)\frac{d\, u(x)}{x} \right] \right}_i = \frac{[A(x)\frac{d\, u(x)}{x}]_{i+1/2} - [A(x)\frac{d\, u(x)}{x}]_{i-1/2}}{h} = [ /tex ]

    [ tex ] = \frac{A_{i+1/2}\[\frac{u_{i+1}-u_{i}}{h}\] - A_{i-1/2}\[\frac{u_{i}-u_{i-1}}{h}\]}{h} [ /tex ]

    So, if I use centered differences I would have to have values for A at i + 1/2 and A at i - 1/2; is that correct? If I use forward or backward differences I need A values at i, i + 1, i + 2 and at i, i -1, i -2 respectively.

    Am I on the correct path?

    I would really appreciate any hint.

    Thanks in advance,

    Federico
     
  2. jcsd
  3. Aug 26, 2011 #2

    Stephen Tashi

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    Science Advisor

    I think your LaTex expressions would show up correctly if you omit the space between the brackets around the tex tags and what is inside the tag.
     
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