Function composition in finite differences

[fmilano]

Hi. I am trying to express the following in finite differences:

[ tex ] \frac{d}{x}\left[ A(x)\frac{d\, u(x)}{x} \right] [ /tex ]

If I take centered differences I get:

[ tex ] \left{ \frac{d}{x}\left[ A(x)\frac{d\, u(x)}{x} \right] \right}_i = \frac{[A(x)\frac{d\, u(x)}{x}]_{i+1/2} - [A(x)\frac{d\, u(x)}{x}]_{i-1/2}}{h} = [ /tex ]

[ tex ] = \frac{A_{i+1/2}\[\frac{u_{i+1}-u_{i}}{h}\] - A_{i-1/2}\[\frac{u_{i}-u_{i-1}}{h}\]}{h} [ /tex ]

So, if I use centered differences I would have to have values for A at i + 1/2 and A at i - 1/2; is that correct? If I use forward or backward differences I need A values at i, i + 1, i + 2 and at i, i -1, i -2 respectively.

Am I on the correct path?

I would really appreciate any hint.

Thanks in advance,

Federico

 

[Stephen Tashi]

I think your LaTex expressions would show up correctly if you omit the space between the brackets around the tex tags and what is inside the tag.