Finite differences for PDE

  • Thread starter Shade
  • Start date
  • #1
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Homework Statement


Show that the first order derivative y'(xi) in the point xi may be approximated by

y'(xi)= (1/12*h) * (-3yi-1 -10yi + 18yi+1 -6yi+2 + yi+3) - (1/20h) h^4*y^(5) + O(h^5)


The Attempt at a Solution



I think the idea is to setup a linear system and some how use taylor expansion.

y'(xi) = a(-1)*y(xi-1) +
a(0) *y(xi) +
a( 1) *y(xi+1) +
a( 2) *y(xi+2) +
a( 3) *y(xi+3) +

Anyone has any idea on how I can show the above?
 

Answers and Replies

  • #2
HallsofIvy
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xi is a point in how many dimensions? 2, 3?
 
  • #3
13
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I would assume one dimension.

xi are discrete points.

If anyone has any ideas on how to solve this please shout ;-)
 
Last edited:
  • #4
13
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If you can give a hint for n-dimensions HallsofIvy then I am sure I can solve it for 1d ;-)
 

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