Molecular dynamics computer simulation methods are very important for understanding mechanisms of chemical, physical, and biological processes. The reliability of molecular dynamics simulations strongly depends on the integration schemes used in the simulations. In this work, we developed new rigid body integration schemes for molecular dynamics simulations. Our approach is based on a numerical...

Most analytical models include variables that have randomness or uncertainties associated with them. These models span many scientific and engineering disciplines. Analyzing these models without incorporating the uncertainties may provide misleading results. In this paper, several methods for evaluating uncertainty are summarized. One of these methods is illustrated using the Lotus 1-2-3 spread...

We study the resource calculus, an extension of the λ-calculus allowing to model resource consumption. We achieve an internal separation result, in analogy with Böhm’s theorem of λ-calculus. We define an equivalence relation on the terms, which we prove to be the maximal non-trivial congruence on normalizable terms respecting β-reduction. It is significant that this equivalence extends the usua...

We use elliptic Taylor series expansions and interpolation to deduce a number of summations for elliptic hypergeometric series. We extend to the well-poised elliptic case results that in the q-case have previously been obtained by Cooper and by Ismail and Stanton. We also provide identities involving S. Bhargava’s cubic theta functions.

A systematic method for the derivation of high order schemes for affinely controlled nonlinear systems is developed. Using an adaptation of the stochastic Taylor expansion for control systems we construct Taylor schemes of arbitrary high order and indicate how derivative free Runge-Kutta type schemes can be obtained. Furthermore an approximation technique for the multiple control integrals appe...

Under certain conditions the signature method suggested by Pantiledes and Pryce facilitates the local expansion of DAE solutions by Taylor polynomials of arbitrary order. The successive calculation of Taylor coefficients involves the solution of nonlinear algebraic equations by some variant of the Gauss-Newton method. Hence, one needs to evaluate certain Jacobians and several right hand sides. ...

Hermite polynomials arise when dealing with functions of normally distributed variables, and are commonly thought as the analog simple on regular variables. Therefore expansion should be an Taylor expansion. Indeed there is a strong connection between two – general coefficient in weighted integral nth derivative, compared to derivative evaluated at zero case Taylor. This fact can used derive fo...

The Taylor model [8] is one of the inclusion functions available to compute the range enclosures. It has the property of (m+ 1) convergence order, where, m is the order of the Taylor model used. It computes a high order polynomial approximation to a multivariate Taylor expansion, with a remainder term that rigorously bound the approximation error. The sharper bounds on the enclosures computed u...