How to define finite difference approximation for first order derivative

asked 2016-01-25 19:09:28 +0100

Orange
23 ●1 ●5

updated 2022-10-15 13:30:18 +0100

FrédéricC

4893 ●3 ●41 ●104

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 +0100

tmonteil
27083 ●31 ●196 ●510 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 +0100 )edit

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