Phase-lag Analysis for Symmetric Two-Step Methods

1 Phase-lag Analysis for Symmetric Two-Step Methods. - In this section we will study the numerical solution of the problem 

Stability analysis of methods for solving the above initial-value problem has been performed by Lambert and Watson,57 in which they introduce the scalar test equation 

Definition 3. Following Lambert and Watson57 we say that the numerical 

Using these definitions, we have the following theorems (for the proofs see ref. 59)  

Definition 5.60 For any method corresponding to the characteristic equation (132) the quantity 

---