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Elliptic partial differential equation

  1. Jan 25, 2016 #1

    ATY

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    Hey guys, so my professor told me to take a look at an equation, because he thinks that there is a mistake. We are basically talking about exercise 6.3 (on last image). The pictures will show you the text, so that you have all the information, that I have
    11568ce5b2.png
    http://puu.sh/mrNDl/ec19cdff63.png [Broken]
    8d9fc16cc0.png
    http://puu.sh/mrNF3/7461f97ad4.png [Broken]

    So... I should "just use" 6.12 and 6.15 to get 6.16.
    The point is that I have no clue how to do this.
    my attemp was
    http://puu.sh/mJ1HR/08899e8813.png [Broken]
    but, this gets super ugly when I start to insert the phi' from 6.15 and calculate everything. Is this even the right idea ?
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Jan 26, 2016 #2

    haruspex

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    I would concentrate on collecting up terms so that you get a lot of occurrences of ##\phi'_i-\phi_i##, and likewise with i-1.
    You will find terms like ##(\phi'_i\phi'_{i-1}-\phi_i\phi_{i-1})##. Here you can use 2(ab-cd)=(a-c)(b+d)+(a+c)(b-d).
     
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