We present hidden veri cation as a means to make the power of computational logic available to users of computer algebra systems while shielding them from its complexity. We have implemented in PVS a library of facts about elementary and transcendental functions, and automatic procedures to attempt proofs of continuity, convergence and di erentiability for functions in this class. These are cal...

A 2nd-order, L-stable Rosenbrock method from the eld of sti ordinary di erential equations is studied for application to atmospheric dispersion problems describing photochemistry, advective and turbulent di usive transport. Partial di erential equation problems of this type occur in the eld of air pollution modelling. The focal point of the paper is to examine the Rosenbrock method for reliable...

The reliability of dynamic systems modeled by white noise excited, stochastic, ordinary di erential equations can be computed from deterministic backward Kolmogorov equations. This paper discusses and compares some numerical solution methods for boundary value problems involving backward Kolmogorov equations. The numerical examples concern single degree of freedom oscillators subjected to white...

It is proven that an initial value problem of an autonomous system verifying some conditions has exactly one open continuously di€erentiable trajectory on R, whose limit set is not one point. The proof of the result is based upon continuation methods. 1. Preliminaries Di€erential equations play a key role in nature and technology because they control their processes. In time-dependent processes...

The paper describes the aeroelastic analysis of a tiltrotor con guration. The 1/5 scale wind tunnel semispan model of the V-22 tiltrotor aircraft is considered. The analysis is performed by means of a multi-body code, based on an original formulation. The di erential equilibrium problem is stated in terms of rst order di erential equations. The equilibrium equations of every rigid body are writ...

This review focusses on modelling of signal transduction pathways. It will introduce the general concepts of modelling and signal transduction, and then proceed with presenting the two most common approaches: Ordinary Di erential Equations (ODE) and Petri Nets (PN). Including an overview about some of the PN upgrades, such as Timed or Coloured Petri Nets, this review will show the major di eren...

We detail the implementation of basic operations on multivariate Chebyshev approximations. In most cases, they can be derived directly from well known properties of univariate Chebyshev polynomials. Besides addition, subtraction and multiplication, we discuss integration, indefinite di↵erentiation, indefinite integration and interpolation. The latter three, can be written as matrix-vector produ...

We prove that the solution of a system of random ordinary di erential equations dX(t) dt = V(t;X(t)) with di usive scaling, X"(t) = "X( t " ), converges weakly to a Brownian Motion when " # 0. We assume that V(t;x), t 2 R, x 2 R is a d-dimensional, random, incompressible, stationary Gaussian eld which has mean zero and decorrelates in nite time.

Lie Analysis of Diierential Equations (D.E.) is based on the symmetries of D.E. and their integral curves. The method looks for new variables, called canonical variables, which straighten out the group action. This article is devoted to explain what are those variables and why they simplify the D.E., trying to strike a balance between the original avor of Lie's idea and the algorithm usually pr...

This paper is concerned with time-stepping numerical methods for computing sti semi-discrete systems of ordinary di erential equations for transient hypersonic ows with thermo-chemical nonequilibrium. The sti ness of the equations is mainly caused by the viscous ux terms across the boundary layers and by the source terms modeling nite-rate thermo-chemical processes. Implicit methods are needed ...