Numerical Analysis/stability of RK methods/exercises

Exercises

Ex:1

find the stability function for RK2 which is given by: ${\displaystyle y_{n+1}=y_{n}+hf(t+{\frac {h}{2}},y_{n}+{\frac {hf(t_{n},y_{n})}{2}})}$

Ex:2

find the absolute stability region for RK2.

Ex:3

find the characteristic polynomial for RK2.

Ex:4

is RK2 stable, if it is what type of stability.

Ex:5

Determine the stability of Back ward Euler method.