We describe the derivation of order conditions, without restrictions on stage order, for general linear methods for ordinary differential equations. This derivation is based on the extension of Albrecht approach proposed in the context of Runge-Kutta and composite and linear cyclic methods. This approach was generalized by Jackiewicz and Tracogna to two-step Runge-Kutta methods, by Jackiewicz a...

In the paper we discuss the transition from kinetic theory to macroscopic uid equations, where the macroscopic equations are deened as asymptotic limits of a kinetic equation. This relation can be used to derive computationally eecient domain decomposition schemes for the simulation of rareeed gas ows close to the continuum limit. Moreover, we present some basic ideas for the derivation of kine...

This work generalizes the additively partitioned Runge-Kutta methods by allowing for different stage values as arguments of different components of the right hand side. An order conditions theory is developed for the new family of generalized additive methods, and stability and monotonicity investigations are carried out. The paper discusses the construction and properties of implicit-explicit ...

Some biomechanical models are represented by nonlinear first order ordinary differential equations. The objective of this study is to determine the velocity of a biomechanical model that involves a cyclist coasting downhill. Two methods namely; the modified explicit and diagonally implicit fifth–order Runge–Kutta methods are utilised. The performance of the two methods is compared with the exac...

This article presents how various Formal Methods have been involved, rst on their own, then coupled, in the diierent steps of the industrial development of an embedded software for an electricity meter. Synchronized Transition Systems have been used to conceive and implement some Rendezvous mechanisms for the distributed kernel , and the physical link protocol supporting communication between p...

In this note we propose and analyze an implicit-explicit scheme based on second order strong stability preserving time discretisations. We also present some theoretical and numerical stability results for second order Runge Kutta IMEX schemes.

The primary goal of this work is to introduce two adaptive Steffensen-like methods with memory of the highest efficiency indices. In the existing methods, to improve the convergence order applied to memory concept, the focus has only been on the current and previous iteration. However, it is possible to improve the accelerators. Therefore, we achieve superior convergence orders and obtain as hi...