Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of
interacting electronic many-body systems formally exactly and in a practical and efficient …

Approximate resolution of linear systems of differential equations with varying coefficients is
a recurrent problem, shared by a number of scientific and engineering areas, ranging from …

The ubiquity of semilinear parabolic equations is clear from their numerous applications
ranging from physics and biology to materials and social sciences. In this paper, we …

This book evolved from lecture notes developed over the past 20+ years of teaching this
material, mostly in Applied Mathematics 585–6 at the University of Washington. The course …

Functions of matrices have been studied for as long as matrix algebra itself. Indeed, in his
seminal A Memoir on the Theory of Matrices (1858), Cayley investigated the square root of a …

In principle, the exponential of a matrix could be computed in many ways. Methods involving
approximation theory, differential equations, the matrix eigenvalues, and the matrix …

In this paper we consider the construction, analysis, implementation and application of
exponential integrators. The focus will be on two types of stiff problems. The first one is …

A modification of the exponential time-differencing fourth-order Runge--Kutta method for
solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in …

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it
computes either a small matrix exponential in full, the action of a large sparse matrix …

We present and discuss a framework for computer-aided multiscale analysis, which enables
models at a fine (microscopic/stochastic) level of description to perform modeling tasks at a …