arXiv subjects

Aleksandr A. Shemendyuk

Publications and source records attributed to Aleksandr A. Shemendyuk.

2 recordsLinked to original sources

arXiv2020

Discrete Transparent Boundary Conditions for the Equation of Rod Transverse Vibrations

Local perturbations of an infinitely long rod go away to infinity. On the contrary, in the case of a finite length of the rod, the perturbations reach its boundary and are reflected from it. The boundary conditions constructed here for the implicit difference scheme imitate the Cauchy problem and provide almost no reflection. These boundary conditions are non-local in time, and their practical implementation requires additional calculations at every time step. To minimise them, a special rational approximation similar to the Hermite - Padé approximation is used. Numerical experiments confirm the high "transparency" of these boundary conditions and determine the conditional stability regions for finite-difference scheme.

math.NA↗

arXiv2019

Fair Insurance Premium Level in Connected SIR Model under Epidemic Outbreak

In this paper we aim to study an optimal insurance premium level for health-care in a deterministic and stochastic SIR models with migration fluxes and vaccination of population. The studied model considers two standard SIR centres connected via links and continuous migration fluxes. The premium is calculated using the basic equivalence principle. Even in this simple setup there are non-intuitive results that illustrate how the premium depends on migration rates, severeness of a disease and initial distribution of healthy and infected individuals through the centres. We investigate how the vaccination program effects the insurance costs by comparing the savings in benefits with the expenses for vaccination. We compare the results of deterministic and stochastic models.

q-bio.PE↗