How to define finite difference approximation for first order derivative

asked 2016-01-25 12:09:28 -0500

Orange
11 ●1

updated 2016-01-26 02:00:49 -0500

tmonteil
13378 ●18 ●95 ●240 http://wiki.sagemath.o...

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 -0500

tmonteil
13378 ●18 ●95 ●240 http://wiki.sagemath.o...

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 ( 2016-01-28 06:14:29 -0500 )edit

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Asked: 2016-01-25 12:09:28 -0500

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Last updated: Jan 26 '16

How to define finite difference approximation for first order derivative

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