How to define finite difference approximation for first order derivative

asked 2016-01-25 19:09:28 +0200

Orange
23 ●1 ●5

updated 2022-10-15 13:30:18 +0200

FrédéricC

5125 ●3 ●43 ●111

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?

answered 2016-01-26 09:22:44 +0200

tmonteil
27323 ●31 ●202 ●514 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 13:14:29 +0200 )edit

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