A new approach to design A-stable linear multistep integration algorithms

Linear multistep (LMS) integration formulas are frequently applied to the numerical solution of differential equations. If the used LMS integration formula complies with a particular kind of numerical stability, so-called A-stability, the simulation algorithm of a physical system will be stable. A-stability turns out to be contrary to a most used definition of mathematical accuracy for these formulas. Moreover, LMS integration formulas may also be considered from the point of view of electrical network theorems. This approach leads to a new approximation, which is similar to the filter design problem and which is not in contradiction to the A-stability requirement of integration formulas