On stable numerical integration methods of maximum time step

Abstract

Two new three step formulae are introduced for the numerical integration of a first order ordinary differential equation. One is implicit and the second explicit. Each is optimal in the sense of permitting the maximum time steps under which the numerical integration formula is numerically stable when applied to a standard reference equation. For example, the maximum admissible time steps in the optimal methods are several times greater than those of the Adams-Bashforth explicit and Adams-Moulton implicit methods.