Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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,

  2. jcsd
  3. Aug 26, 2011 #2

    Stephen Tashi

    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook