Hi everyone:(adsbygoogle = window.adsbygoogle || []).push({});

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):

u_{1}^{k+1}= (u_{1}^{k}- a(0, t^{k+1})/d

u_{2}^{k+1}= (u_{2}^{k}- a(0, u_{1}^{k+1})/d

u_{i}^{k+1}= (u_{i}^{k}- a(0, u_{i-1}^{k+1})/d

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

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