A review is given on the multiconfiguration time-dependent Hartree (MCTDH) method, which
is an algorithm for propagating wavepackets. The formal derivation, numerical …

Recently, there has been a great deal of interest in the construction of exponential
integrators. These integrators, as their name suggests, use the exponential function (and …

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 …

The first book dedicated to this new and powerful computational method begins with a
comprehensive description of MCTDH and its theoretical background. There then follows a …

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 …

In this note a theoretical analysis of some Krylov subspace approximations to the matrix
exponential operation \exp(A)v is presented, and a priori and a posteriors error estimates …

Krylov subspace methods for approximating the action of matrix exponentials are analyzed
in this paper. We derive error bounds via a functional calculus of Arnoldi and Lanczos …

We study the numerical integration of large stiff systems of differential equations by methods
that use matrix--vector products with the exponential or a related function of the Jacobian …

This paper takes a new look at numerical techniques for solving parabolic equations by the
method of lines. The main motivation for the proposed approach is the possibility of …

In this paper we present a simple, general methodology for the generation of high-order
operator decomposition (“splitting”) techniques for the solution of time-dependent problems …