Research of the process of radon accumulation in the accumulating chamber taking into account the nonlinearity of its entrance

Tverdyi, Dmitriy; Parovik, Roman; Makarov, Evgeniy; Фирстов, П. П.

doi:10.1051/e3sconf/202019602027

Cited by 9 publications

(1 citation statement)

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“…It can be concluded that an explicit finite-difference scheme can be used to calculate dynamic processes in environments with saturation. Further continuation of the work lies is the practical application of an explicit finite-difference scheme for calculating the curves of the volumetric activity of radon in a storage chamber by analogy with work [36].…”

Section: Discussionmentioning

confidence: 99%

Some Aspects of Numerical Analysis for a Model Nonlinear Fractional Variable Order Equation

Parovik

Tverdyi

2021

MCA

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The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of a nonlinear, ordinary differential equation with a derivative of a fractional variable order of the Gerasimov–Caputo type. The questions of approximation, convergence, and stability of this scheme are studied. It is shown that the nonlocal finite-difference scheme is conditionally stable and converges to the first order. Using the fractional Riccati equation as an example, the computational accuracy of the numerical method is analyzed. It is shown that with an increase in the nodes of the computational grid, the order of computational accuracy tends to unity, i.e., to the theoretical value of the order of accuracy.

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Section: Discussionmentioning

confidence: 99%