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I cannot grasp a lot of concepts, but here's some I'd like to at least get an idea of:

Factorization method. I only scrapped that it is a special case of Gauss' Exclusion method, that you take a 2nd order difference and turn it into three 1st order differences (or 4th order difference to turn into five 2nd order differences I guess). But I simply could not follow the math. Very with playing with coefficients and this "recurrence equation" that goes like this. $$y_i=\alpha_{i+1}y_{i+1}+\beta_{i+1}$$

and they're put into some mysterious $$A_iy_{i-1}-C_i y_i + B_i y_{i+1}=-F_i; i=1,2,...,N-1$$

And later on some big importance is given to this $$|C_i|\geqslant|A_i|+|B_i|$$

And I really don't know anything about stability. It's the first thread I made here, too. But yeah I can't find any materials that would actually explain to me what stability is and how the various elements like those eigenvalues $\lambda$ and eigenfunctions and whatnot come into play with it.

I guess that's all I can muster to write now.