find the stability function for RK2 which is given by:
applying this method to the test equation
- we get
the stability polynomial
find the absolute stability region for RK2.
- the abs.stability region is given by
find the characteristic polynomial for RK2.
divide both sides of the equation by
is RK2 stable, if it is what type of stability.
by setting z=0,
- so the method is strongly stable since r=1, is the only root, and has a value of 1.
Determine the stability of Back ward Euler method.
- by applying this method to the test equation
- and so
- call and so:
- and so this is L-Stable method when applied to stiff equation.