21 citations · 68 across the 22 of their papers we have counts for
9 papers · 1 filter
Multi-domain spectral approach for Zakharov-Kuznetsov equations in 3D with cylindrical symmetry
Christian Klein, Svetlana Roudenko, Nikola Stoilov
We present a novel numerical framework for studying nonlinear dispersive equations in higher-dimensional settings, specifically designed for solutions featuring traveling waves alo…
Multi-domain spectral approach to rational-order fractional derivatives
C. Klein, N. Stoilov
We propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is…
Spectral approach to Korteweg-de Vries equations on the compactified real line
C. Klein, N. Stoilov
We present a numerical approach for generalised Korteweg-de Vries (KdV) equations on the real line. In the spatial dimension we compactify the real line and apply a Chebyshev collo…
Multi-domain spectral approach for the Hilbert transform on the real line
C. Klein, J. Riton, N. Stoilov
A multi-domain spectral method is presented to compute the Hilbert transform on the whole compactified real line, with a special focus on piece-wise analytic functions and function…
High precision numerical approach for the Davey-Stewartson II equation for Schwartz class initial data
C. Klein, K. McLaughlin, N. Stoilov
We present an efficient high-precision numerical approach for the Davey-Stewartson (DS) II equation, treating initial data from the Schwartz class of smooth, rapidly decreasing fun…
Numerical study of the transverse stability of the Peregrine solution
C. Klein, N. Stoilov
We generalise a previously published approach based on a multi-domain spectral method on the whole real line in two ways: firstly, a fully explicit 4th order method for the time in…
Multidomain spectral method for the Gauss hypergeometric function
S. Crespo, M. Fasondini, C. Klein +2
We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius' m…
Spectral approach to the scattering map for the semi-classical defocusing Davey-Stewartson II equation
C. Klein, K. McLaughlin, N. Stoilov
The inverse scattering approach for the defocusing Davey-Stewartson II equation is given by a system of D-bar equations. We present a numerical approach to semi-classical D-bar pro…
Numerical scattering for the defocusing Davey-Stewartson II equation for initial data with compact support
C. Klein, N. Stoilov
In this work we present spectral algorithms for the numerical scattering for the defocusing Davey-Stewartson (DS) II equation with initial data having compact support on a disk, i.…