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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…