Module 8: Linear Multistep Methods
  Lecture 30: Absolute Stability and Relative Stability
 

 

Hence

(8.30)

We now make two important simplifying assumptions:

, Constant

Constant

The equation for now reduces to the linearized error equation

(8.31)

The general solution of this equation is

(8.32)

where the are arbitrary constants and the are the roots, assumed distinct, of the polynomial equation

(8.33)