In this paper, we propose new variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods for the numerical integration of ordinary differential equations (ODEs). The methods are constructed geometrically from an exponentially fitted osculating parabola. The accuracy and stability of the proposed variants is discussed and their applicability to some initial value problems is...

The symplectic group Sp(4, F ) has a particular interesting unitary representation for F a finite or local field. When F is finite this representation was denoted Θ10 [30], and somehow the name has stuck. We discuss this representation in some detail in the case of R. This material is mostly well known, at least to the experts, and this paper is intended as a reference for non–specialists. It a...