Characteristic methods for multidimensional evolution equations

Pseudospectral Differencing Methods for Characteristic Roots of Delay Differential Equations

In [BMV03]and [Bre02] the authors proposed to compute the characteristic roots of Delay Differential Equations (DDEs) with multiple discrete and distributed delays by approximating the derivative in the infinitesimal generator of the solution operator semigroup by Runge-Kutta (RK) and Linear Multistep (LMS) methods, respectively. In this work the same approach is proposed in a new version based...

Characteristic Methods for Fokker-Planck and Fermi Pencil Beam Equations

Constraint-Preserving Upwind Methods for Multidimensional Advection Equations

A general framework for constructing constraint-preserving numerical methods is presented and applied to a multidimensional divergence-constrained advection equation. This equation is part of a set of hyperbolic equations that evolve a vector field while locally preserving either its divergence or curl. We discuss the properties of these equations and their relation to ordinary advection. Due t...

Laplace Transform Methods for Evolution Equations

The Laplace transform theory of Banach space valued functions and the field of evolution equations presently offer many research problems which are of general interest in mathematical analysis. Although there is a longstanding relationship between the two fields, it was not until recently that the basic transform principles for Banach space valued functions could be formulated in a satisfactory...

Semigroup methods for evolution equations on networks

1 2 These notes derive from the lecture series " Evolution equations on networks " , held in March 2007 at the Mathematical Department at Lousiana State University and are sporadically updated. The lectures were conceived with the aim of presenting known results obtained over the last few years by a group of few researchers with a definite operator theoretical background, most of whom currently...