Interactions are explored through the observation of the dynamics of particles. On the classical level the basic underlying assumption in that scheme is that Newton's second law holds. Relaxing the validity of this axiom by, e.g., allowing for higher order time derivatives in the equations of motion would allow for a more general structure of interactions. We derive the structure of interaction...

Keywords: Ordinary differential equations Runge–Kutta methods One-step methods Hamiltonian problems Hamiltonian Boundary Value Methods Energy preserving methods Symplectic methods Energy drift a b s t r a c t In this paper, we provide a simple framework to derive and analyse a class of one-step methods that may be conceived as a generalization of the class of Gauss methods. The framework consis...

This paper describes a study of a class of algorithms for the floating-point divide and square root operations, based on the Newton-Raphson iterative method. The two main goals were: (1) Proving the IEEE correctness of these iterative floating-point algorithms, i.e. compliance with the IEEE-754 standard for binary floating-point operations [1]. The focus was on software driven iterative algorit...

We present techniques for implicit solution of discontinuous Galerkin discretizations of the Navier-Stokes equations on parallel computers. While a block-Jacobi method is simple and straight-forward to parallelize, its convergence properties are poor except for simple problems. Therefore, we consider Newton-GMRES methods preconditioned with block-incomplete LU factorizations, with optimized ele...

I N T R O D U C T I O N While issues related to the operating pattern (scheduling) of batch plants have been extensively studied in the open literature, the problem of accounting for equipment (un)availability and systems effectiveness under changing conditions has received much less attention despite its enormous practical significance (Straub and Grossmann, 1992; Subrahmanyam et al., 1994; Sa...

We revisit the problem of extending quadrature formulas for general weight functions, and provide a generalization of Patterson’s method for the constant weight function. The method can be used to compute a nested sequence of quadrature formulas for integration with respect to any continuous probability measure on the real line with finite moments. The advantages of the method include that it w...