Module 8: Linear Multistep Methods
  Lecture 31: General methods for finding intervals of absolute and relative stability
 

 

Example: Use the Schur criterion to investigate the weak stability of the method

Solution: The stability polynomial is

. Thus,

and the condition is

satisfied if , that is, if

Now

which has its only root at and is therefore a Schur polynomial. It follows that the interval of absolute stability is .