1 citations · 1 across the 8 of their papers we have counts for
8 papers
On a class of modified Cayley--Magnus methods
Sergio Blanes, Fernando Casas, Arieh Iserles
We introduce a new class of numerical integrators for the time integration of non-autonomous linear ordinary differential equations whose coefficient matrix is sparse and evolves w…
On semi-separability and differentiation matrices
Arieh Iserles
The theory of spectral methods for partial differential equations leads to infinite-dimensional matrices which represent the derivative operator with respect to an underlying ortho…
Fourth-order compact exponential splittings for unbounded operators
Juan Carlos Del Valle, Arieh Iserles, Karolina Kropielnicka
We present a derivation and error bound for the family of fourth order splittings, originally introduced by Chin and Chen, where one of the operators is unbounded and the second on…
Convergence of a moving window method for the Schrödinger equation with potential on
Arieh Iserles, Buyang Li, Fangyan Yao
We propose a novel framework, called moving window method, for solving the linear Schrödinger equation with an external potential in . This method employs a smooth cu…
Computation of some dispersive equations through their iterated linearisation
Guannan Chen, Arieh Iserles, Karolina Kropielnicka +1
It is often the case that, while the numerical solution of the non-linear dispersive equation represents a formidable challenge,…
An accelerated Levin-Clenshaw-Curtis method for the evaluation of highly oscillatory integrals
Arieh Iserles, Georg Maierhofer
The efficient approximation of highly oscillatory integrals plays an important role in a wide range of applications. Whilst traditional quadrature becomes prohibitively expensive i…
Splitting methods for unbounded operators
Arieh Iserles, Karolina Kropielnicka
This paper considers computational methods that split a vector field into three components in the case when both the vector field and the split components might be unbounded. We fi…
An elementary approach to splittings of unbounded operators
Arieh Iserles, Karolina Kropielnicka
Using elementary means, we derive the three most popular splittings of and their error bounds in the case when and are (possibly unbounded) operators in a Hilbe…