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What I want to ask here is, what is the fastest way usually to solve difference equation? I know how to do the sort of coefficient thing with lambdas, but am not sure bout smth in my notes... kinda the other way.
Here it is:
Xn+2 - 3Xn+1 + 2Xn=0, X0=0, X1=1.
Let Vn=(Xn)
...........(Xn+1)
Vn+1=(Xn+1)=( Xn+1)..........=(0 1) (Xn)
..........(Xn+2)..(3Xn+1 - 2Xn)...(-2 2) (Xn+1)
Vn+1=AVn
A=(0 1)
....(-2 3 ) V0=(0)
.....................(1)
What is the idea behind this? Where does 0 1
..........................................................-2 2
matrix come from and why does it change to 3 down there? Is there smth wrong here? Is this a general way of solution?
Most importantly, how do I get matrix A out of difference equation when i solve? Down from here, it's just diagonalization... that I can do.
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