We consider the combustion equation as one of the candidates from the class of stiff ordinary differential equations. A solution over a length of time that is inversely proportional to δ > 0 (where δ > 0 is a small disturbance of the pre-ignition state) is sought. This problem has a transient at the midpoint of the integration interval. The solution changes from being non-stiff to stiff, and af...

The natural stiffness of DNA, which contributes to the interactions of the many proteins involved in its biological processing and packaging, also plays an important role in modern nanotechnology. Here we report new Monte-Carlo simulations of deformable DNA molecules of potential utility in understanding the behavior of the long, double-helical polymer in the tight confines of a cell and in the...

Neumaier’s Method For The Solution Of Initial Value Problems For Stiff Ordinary Differential Equations Annie Hsiao Chen Yuk Master of Science Graduate Department of Computer Science University of Toronto 2005 Compared with standard numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs), validated methods not only compute a numerical solution to a problem,...

In this paper we will derive an implicit-explicit (IMEX) finite volume evolution Galerkin scheme for three-dimensional Euler equations. We will in particular concentrate a singular limit of weakly compressible flows when the Mach number is about O(10−2)−O(10−6). In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gr...

A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state P = ρ. A wide class of self-similar solutions turn out to be unstable against kink mode perturbation. According to the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be a critical solutio...