2800	 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 -stability. It is shown that for p k k arbitrary A inf -stability implies certain necessary conditions for A -stability and for strict stability meaning that the extraneous roots of p psi satisfy psi for p k and A inf -stability for k together with another constraint implies strict stability and for certain one-parameter classes of formulas with p k and or A inf -stability implies A -stability. stiff equations parametrized linear multistep formulas order of accuracy A -stability A inf -stability strict stability
