The Magnus expansion and some of its applications
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 …
a recurrent problem, shared by a number of scientific and engineering areas, ranging from …
[BOOK][B] Spectral and dynamical stability of nonlinear waves
T Kapitula, K Promislow - 2013 - Springer
The stability of nonlinear waves has a distinguished history and an abundance of richly
structured yet accessible examples, which makes it not only an important subject but also an …
structured yet accessible examples, which makes it not only an important subject but also an …
Evans functions for integral neural field equations with Heaviside firing rate function
In this paper we show how to construct the Evans function for traveling wave solutions of
integral neural field equations when the firing rate function is a Heaviside. This allows a …
integral neural field equations when the firing rate function is a Heaviside. This allows a …
Fourth-and sixth-order commutator-free Magnus integrators for linear and non-linear dynamical systems
We present a family of numerical integrators based on the Magnus series expansions which
is designed for solving non-autonomous differential equations. The main difference with …
is designed for solving non-autonomous differential equations. The main difference with …
Computing the Maslov index for large systems
We address the problem of computing the Maslov index for large linear symplectic systems
on the real line. The Maslov index measures the signed intersections (with a given reference …
on the real line. The Maslov index measures the signed intersections (with a given reference …
Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations
JA Sherratt - Advances in Computational Mathematics, 2013 - Springer
A variety of numerical methods are available for determining the stability of a given solution
of a partial differential equation. However for a family of solutions, calculation of boundaries …
of a partial differential equation. However for a family of solutions, calculation of boundaries …
Finding eigenvalues of holomorphic Fredholm operator pencils using boundary value problems and contour integrals
WJ Beyn, Y Latushkin, J Rottmann-Matthes - Integral equations and …, 2014 - Springer
Investigating the stability of nonlinear waves often leads to linear or nonlinear eigenvalue
problems for differential operators on unbounded domains. In this paper we propose to …
problems for differential operators on unbounded domains. In this paper we propose to …
Grassmannian spectral shooting
V Ledoux, S Malham, V Thümmler - Mathematics of Computation, 2010 - ams.org
We present a new numerical method for computing the pure-point spectrum associated with
the linear stability of coherent structures. In the context of the Evans function shooting and …
the linear stability of coherent structures. In the context of the Evans function shooting and …
On the method of Neumann series for highly oscillatory equations
A Iserles - Bit Numerical Mathematics, 2004 - Springer
The main purpose of this paper is to describe and analyse techniques for the numerical
solution of highily oscillatory ordinary differential equations by exployting a Neumann …
solution of highily oscillatory ordinary differential equations by exployting a Neumann …
Efficient strong integrators for linear stochastic systems
We present numerical schemes for the strong solution of linear stochastic differential
equations driven by an arbitrary number of Wiener processes. These schemes are based on …
equations driven by an arbitrary number of Wiener processes. These schemes are based on …