4 citations · 5 across the 8 of their papers we have counts for
5 papers · 1 filter
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…
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…
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…