4 citations · 5 across the 8 of their papers we have counts for
8 papers
Time-Dependent Logarithmic Perturbation Theory for Quantum Dynamics: Formulation and Applications
Juan Carlos del Valle, Paul Bergold, Karolina Kropielnicka
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schrödinger equation, in which the logarithm of the wa…
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…
Correlations and signaling in the Schrödinger-Newton model
Jacek Aleksander Gruca, Ankit Kumar, Ray Ganardi +3
The Schrödinger--Newton model is a semi-classical theory in which, in addition to mutual attraction, massive quantum particles interact with their own gravitational fields. While t…
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,…
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…
Asymptotic expansions for the linear PDEs with oscillatory input terms; Analytical form and error analysis
Karolina Kropielnicka, Rafał Perczyński
Partial differential equations with highly oscillatory input terms are hardly ever solvable analytically and their numerical treatment is difficult. Modulated Fourier expansion use…
Second-order exponential splittings in the presence of unbounded and time-dependent operators: construction and convergence
Karolina Kropielnicka, Juan Carlos del Valle
For linear differential equations of the form , , with a possibly unbounded operator , we construct and deduce error bounds for two families of se…