1 the A-stability is characterized by:
2 Euler method is:
3 the absolute stability region for RK4 is greater than the A-stability region for the same method:
4 A numerical method is stable if :
5 λ = 1 {\displaystyle \lambda =1} is always a root of the characteristic polynomial of the multistep method:
6 the root of the C.P. can be real or complex,and the method still be stable:
7 A multi- step method is strongly stable if :
8 if more than one root has magnitude equal to 1, and the others are less than one, the method is
9 The numerical method is unstable if
10 the absolute stabity region for the explicit Euler's method is
11 None of the RK methods is A-Stable:
12 All explicit methods are :
13 implicit multistep methods are A-stable if the have order at most