Abstract
This paper is concerned with deriving necessary and sufficient conditions for multistep methods to be convergent. The conditions require that the zeros of an analytic function defined by a determinant of analytic functions all lie outside the unit circle. It is demonstrated that this condition is equivalent to the eigenvalue condition obtained in a previous paper (Holyhead, McKee and Taylor (1975)). The concepts of strong and weak stability are also introduced. A weakly stable method is given.
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