General Form of Multistep Methods

The general form of a linear multistep method reads 

We associate with a fc-step method a pair (p, a) of generating polynomials of order k by setting 

We will discuss later the stability of a multistep method in terms of roots of these polynomials. 

Though this notation originates from the theory of difference operators, we refrain from formally introducing difference operators in this book. 

It will be clear from the context if p and g denote polynomials or are used in the sense of convention (4.1.13). 

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