Connections Between Accuracy and Stability
Properties of Linear Multistep Formulas

This paper is concerned with stability and accuracy
of families of linear k-step formulas depending 
on parameters, with particular emphasis on the numerical
solution of stiff ordinary differential equations. 
 An upper bound, p=k, is derived for the order of accuracy
of A(inf)-stable formulas.  Three criteria 
are given for A(0)-stability.  It is shown that (1) for
p=k, k arbitrary, A(inf)-stability implies certain 
necessary conditions for A(0)-stability and for strict
stability (meaning that the extraneous roots of 
p(psi) satisfy |psi|<1); (2) for p=k=2,3,4,and 5, A(inf)-stability
(for k=5 together with another constraint) 
implies strict stability; and (3) for certain one-parameter
classes of formulas with p=k=3,4,and/or 5, 
A(inf)-stability implies A(0)-stability.

CACM January, 1975

Liniger, W.

stiff equations, parametrized linear multistep formulas,
order of accuracy, A(0)-stability, A(inf)-stability, 
strict stability

5.17

CA750111 JB January 12, 1978  9:26 AM

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