Elliptic partial differential equation

  • #1
ATY
34
1
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 ?
 
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  • #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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