Exponential stability of time-varying linear systems (2009)
Hill, Adrian T., Ilchmann, Achim
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 09-18
Algebraically stable general linear methods and the G-matrix (2009)
Hewitt, Laura L, Hill, Adrian T
The standard algebraic stability condition for general linear methods (GLMs) is considered in a modified form, and connected to a branch of Control Theory concerned with the discrete algebraic...
Dissipativity of Runge-Kutta methods in Hilbert spaces (2007)
: This paper concerns the discretization by Runge-Kutta methods of the initial value problem u t = f(u), under the dissipative structural condition that there exist ff 0; fi ? 0; such that f : W...
Optimal L p estimates for the solutions of elliptic equations in bounded domains (2007)
: Linear second-order elliptic Dirichlet problems are considered in a bounded domain\Omega ae R N . Isoperimetric inequalities are used to obtain sharp estimates of the solution operator from L p to...
The Z-transform and linear multistep stability (2007)
Coughlan, James J., Hill, Adrian T., Logemann, Hartmut
This paper makes systematic use of control-theoretic methods such as the 𝒵-transform, small-gain theorems and frequency-domain stability criteria in the analysis of the stability behaviour of...
The {Zscript}-transform and linear multistep stability (2006)
Coughlan, James J., Hill, Adrian T., Logemann, Hartmut
This paper makes systematic use of control-theoretic methods such as the {Zscript}-transform, small-gain theorems and frequency-domain stability criteria in the analysis of the stability behaviour of...
Multistep approximation of linear sectorial evolution equations (2005)
This paper concerns the linear multistep approximation of a linear sectorial evolution equation ut = Au on a complex Banach space X. Given a strictly A(α)-stable q-step method of order p...
On a multistep method approximating a linear sectorial evolution equation (2002)
Del Buono, Nicoletta, Hill, Adrian T.
This paper concerns the linear multistep approximation of an abstract dissipative linear sectorial evolution equation on a Banach space X. We study how well the semigroup generated by a sectorial...
Approximation of the global attractor for the incompressible Navier-Stokes equations (2000)
This paper considers the asymptotic behaviour of a practical numerical approximation of the Navier–Stokes equations in &OHgr;, a bounded subdomain of 2. The scheme consists of a conforming finite...
Attractors for convection-diffusion equations and their numerical approximation. (1992)
Thesis (Ph. D.)--University of Oxford, 1992.
Attractors for convection-diffusion equations and thier numerical approximation / (1992)
BLDSC reference no.: D171997.
Estimates on the Green's function of second-order elliptic operators in R^N
: Sharp upper and lower pointwise bounds are obtained for the Green's function of the equation (L + )u j \Gamma\Deltau + a(x):ru + u = f; x 2 R N ; for ? 0. Initially in a Cartesian frame it is...
Estimates on the Heat Kernel of Parabolic Equations With Advection
: The paper considers heat kernels of second--order parabolic equations in R N , with constant uniform diffusion and advective coefficients bounded in the maximum norm. Two critical cases,...