827 citations · 846 across the 12 of their papers we have counts for
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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…
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…