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How to define finite difference approximation for first order derivative

asked 2016-01-25 12:09:28 -0600

Orange gravatar image

updated 2016-01-26 02:00:49 -0600

tmonteil gravatar image

I need to define $$y1(k)=\frac{y_{k+1}-y_{k-1}}{2*h}$$

in sage so that sage can differ between symbolic $$y_{k+1}$$ and $$y_{k}$$.

Would somebody please help?

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answered 2016-01-26 02:22:44 -0600

tmonteil gravatar image

The question is not clear to me, why not simply do:

sage: Y = [1,2,4,3,7,2,1]
sage: h = 0.1
sage: [(Y[k+1]-Y[k-1])/h for k in  range(1,len(Y)-1)]
[30.0000000000000,
 10.0000000000000,
 30.0000000000000,
 -10.0000000000000,
 -60.0000000000000]
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$y_{k+1} $ and $y_k$ needs to remain unknown till the formation of equation, so that they can act as variables in the linear system. My interest is to automate the finite difference method in sage. Should I need to define some new data structure. Thanks for responding though!!!

Orange gravatar imageOrange ( 2016-01-28 06:14:29 -0600 )edit

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Asked: 2016-01-25 12:09:28 -0600

Seen: 112 times

Last updated: Jan 26 '16