Forward substitution in this case? Is it as simple as I think it is?

[bzz77]

Hi everyone:

I am very rusty on linear algebra, so apologies if this is a silly question. The question is, in the system below, is it correct to take the calculated value of u_i^k+1 from each PREVIOUS step and simply plug it in at the NEXT step where (a * u_i-1^k+1 is required.

I need to incorporate a finite difference calculation for 1-dimensional advection in some code I'm writing. I have derived the system of equations that I need, but my linear algebra is so rusty that I'm stuck on what to do next/how to actually use them. I'm hoping that the solution I proposed will be sufficient. If it isn't, what method from linear algebra should I use?

I would very much appreciate any help. Thank you all.

Here is the system (a and d are constants that I can specify):

u₁^k+1 = (u₁^k - a(0, t^k+1)/d

u₂^k+1 = (u₂^k - a(0, u₁^k+1)/d

u_i^k+1 = (u_i^k - a(0, u_i-1^k+1)/d

 

[HallsofIvy]

Yes, that is a standard technique.