827 citations · 846 across the 12 of their papers we have counts for
12 papers
Subordination based approximation of Caputo fractional propagator and related numerical methods
Dmytro Sytnyk
In this work, we propose an exponentially convergent numerical method for the Caputo fractional propagator and the associated mild solution of the Cauchy problem with time…
Numerical method for abstract Cauchy problem with nonlinear nonlocal condition
Volodymyr Makarov, Dmytro Sytnyk, Vitalii Vasylyk
Problem for the first order differential equation with an unbounded operator coefficient in Banach space and nonlinear nonlocal condition is considered. A numerical method is propo…
A Lattice Boltzmann Method for Non-Newtonian Blood Flow in Coiled Intracranial Aneurysms
Medeea Horvat, Stephan B. Lunowa, Dmytro Sytnyk +1
Intracranial aneurysms are the leading cause of hemorrhagic stroke. One of the established treatment approaches is the embolization induced by coil insertion. However, the predicti…
Abstract Fractional Cauchy Problem: Existence of Propagators and Inhomogeneous Solution Representation
Dmytro Sytnyk, Barbara Wohlmuth
We consider a Cauchy problem for the inhomogeneous differential equation given in terms of an unbounded linear operator and the Caputo fractional derivative of order $α\in (0,…
Exponentially Convergent Numerical Method for Abstract Cauchy Problem with Fractional Derivative of Caputo Type
Dmytro Sytnyk, Barbara Wohlmuth
We present an exponentially convergent numerical method to approximate the solution of the Cauchy problem for the inhomogeneous fractional differential equation with an unbounded o…
Sinc approximation of algebraically decaying functions
Dmytro Sytnyk
An extension of sinc interpolation on to the class of algebraically decaying functions is developed in the paper. Similarly to the classical sinc interpolation we esta…
Parallel numerical method for nonlocal-in-time Schrödinger equation
Dmytro Sytnyk
We present a new parallel numerical method for solving the non-stationary Schrödinger equation with linear nonlocal condition and time-dependent potential which does not commute wi…
The Luttinger-Kohn theory for multiband Hamiltonians: A revision of ellipticity requirements
Dmytro Sytnyk, Roderick Melnik
Modern applications require a robust and theoretically solid tool for the realistic modeling of electronic states in low dimensional nanostructures. The theory has frui…
Linear nonlocal problem for the abstract time-dependent non-homogeneous Schrödinger equation
Dmytro Sytnyk, Roderick Melnik
A nonlocal-in-time problem for the abstract Schrödinger equation is considered. By exploiting the linear nature of nonlocal condition we derive an exact representation of the solut…
Existence of the solution to a nonlocal-in-time evolutional problem
Dmytro Sytnyk, Volodymyr Makarov, Vitalii Vasylyk
This work is devoted to the study of a nonlocal-in-time evolutional problem for the first order differential equation in Banach space. Our primary approach, although stems from the…
Multiband Hamiltonians of the Luttinger-Kohn Theory and Ellipticity Requirements
Dmytro Sytnyk, Sunil Patil, Roderick Melnik
Modern applications require a robust and theoretically strong tool for the realistic modeling of electronic states in low dimensional nanostructures. The theory has fru…
Fast convergent method for the -point problem in Banach space
Vitalii Vasylyk, Dmytro Sytnyk
The -point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space is considered. An exponentially convergent algorithm is…