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 2800 5 2800 2800 5 2800 2800 5 2800