How to define finite difference approximation for first order derivative

asked 9 years ago

Orange
23 ●1 ●5

updated 2 years ago

FrédéricC

5466 ●4 ●45 ●122

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 9 years ago

tmonteil
27493 ●32 ●205 ●519 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]

link

Comments

$y_{k+1}$ 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 ( 9 years ago )

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