How would i find the range of a for the following method to make it zero stable:
yn+1-(1+a)yn+ayn-1=1/2((3-a)fn-(1+a)fn-1)
I know to prove zero stability I would make h=0 and then use the quadratic formula to find the roots of the equation to show zero stability if r<1. But with 'a' involved how would i go about finding the range? A step by step solution to find the range would be greatly appreciated.