I'm trying to find the general term of the recurrence relations
$\quad a_{n+1}=a_n+\text hb_n$
$\quad b_{n+1}=b_n-\text ha_n $
$\quad a_0=0, \quad b_0=1$
I tried finding the terms, $a_1, \space a_2, \cdots$ so I can find a formula for the general term but it was too long and and I couldn't even find the solution. Is there a better way I can approach it?
To be specific, I found these relations while using the explicit Euler method for solving ODE's on a second order DE. I'm will be working on this a lot and I was wondering if there is a better way to find the general term for these recurrence relations other than checking term by term until I can find a pattern?