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,...

Implicit integration factor (IIF) methods were developed in the literature for solving time-dependent stiff partial differential equations (PDEs). Recently, IIF methods are combined with weighted essentially non-oscillatory (WENO) schemes in [Jiang and Zhang, Journal of Computational Physics, 253 (2013) 368-388] to efficiently solve stiff nonlinear advection-diffusion-reaction equations. The me...

In this paper we construct extrapolated implicit-explicit time stepping methods that allow to efficiently solve problems with both stiff and non-stiff components. The proposed methods can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method of lines framework. These methods are simple to construct, easy to implement and parallelize. We establish the existence of...

Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihed...

Asymptotic behaviour of eigenvalues and eigenfunctions of a stiff problem is described in the case of the fourth-order ordinary differential operator. Considering the stiffness coefficient that depends on a small parameter ε and vanishes as ε → 0 on a subinterval, we prove the existence of low and high frequency resonance vibrations. The low frequency vibrations admit the power series expansion...

We derive exact general solutions (as opposed to attractor particular solutions) and corresponding first integrals for the evolution of a scalar field $\phi$ in universe dominated by background fluid with equation state parameter $w_B$. In addition previously-examined linear [$V(\phi) = V_0 \phi$] quadratic \phi^2$] potentials, we show that exist power law potential $V(\phi) \phi^n$ $n 4(1+w_B)...