A new approach to the synthesis of stiffly stable linear multistep formulas

The analysis of the linear multistep integration formulas is shown to be considerably simplified by associating to each formula a special function termed the canonical fraction. In particular, the canonical fraction approach provides a decoupling of the problem of stability from the problem of accuracy and allows the derivation of most of the properties of -stable and stiffly stable formulas as simple restatements of elementary electrical network theorems. Results obtained tend to show that linear multistep formulas, which are much more efficient than the ones commonly used today, exist.