By adding a suitable real function on both sides of the quadratic Riccati differential equation, we propose a weighted type of Adams-Bashforth rules for solving it, in which moments are used instead of the constant coefficients of Adams-Bashforth rules. Numerical results reveal that the proposed method is efficient and can be applied for other nonlinear problems.

This article presents a few different methods to present a passive walker model in Adams MD R3 software and compares their simulation results to a walker model built in Matlab software. The discontinuous Matlab simulator applies manually entered mathematical equations to describe system dynamics while the Adams simulation software creates the dynamic models automatically. In the Adams simulator...

Using operad methods and functional homology operations, we obtain inductive formulae for the differentials of the Adams spectral sequence of stable homotopy groups of spheres. The Adams spectral sequence was invented by Adams [1] almost fifty years ago for the calculation of stable homotopy groups of topological spaces (in particular, those of spheres). The calculation of the differentials of ...

The SMF methods of Mart n and Ferr andiz [SIAM J. Numer. Anal. 34 (1997) 359-375], for di erential equations of second order, are shown to be equivalent to modi ed Adams methods. This leads to new formulae for the coe cients of those methods, generating functions analogous to those of the Adams methods for equations of rst order, and simpler, more instructive, expressions for the local truncati...