This paper is a continuation of []. The analysis of the modified partial differential equation (MDE) of the constant-wind-speed linear advection equation explicit difference scheme up to the eighth-order derivatives is presented. In this paper the authors focus on the dissipative features of the Beam–Warming scheme. The modified partial differential equation is presented in the so-called Π-form of

We present data-driven modelling of membrane deformation by a hyperelastic nodal force method. We assume that constitutive relations are characterized by tabulated experimental data instead of the conventional phenomenological approach. As experimental data we use synthetic data from the bulge test simulation for neo-Hookean and Gent materials. The numerical study of descriptive and predictive capabilities

The paper presents a new algorithm of exponential transformation and its randomized modification with branching of a Markov chain trajectory for solving the problem of gamma-ray transport. Based on the example of radiation transfer in water, numerical study of presented algorithms is performed in comparison with standard simulation algorithms. The study of the influence of medium stochasticity on the

In this paper we consider a Boltzmann type equation arising in the kinetic vehicle traffic flow model with an acceleration variable. The latter model is improved within the framework of the previously developed approach by introducing a set of random parameters. This enables us to take into account different types of interacting vehicles, as well as various parameters describing skills and behavior

Special discrete and asymptotic approximations are proposed for the boundary value problem describing a stationary radiative–conductive heat transfer in a system of absolutely black heat-conducting rods of circular cross-section. Results of numerical experiments are presented to confirm the efficiency of proposed approximations.

A mathematical model of the dynamics of cardiomyocyte death in myocardial infarction during the acute phase of the disease is developed. An economical computing technology of structural and parametric identification of model equations is presented based on the use of experimental data as dynamic parameters and on the idea of splitting the inverse coefficient problem with a large number of unknown parameters

The problem of guaranteed computation of all steady states of the Marchuk–Petrov model with fixed values of parameters and analysis of their stability are considered. It is shown that the system of ten nonlinear equations, nonnegative solutions of which are steady states, can be reduced to a system of two equations. The region of possible nonnegative solutions is analytically localized. An effective

The analysis of the modified partial differential equation (MDE) of the constant wind speed advection equation explicit difference scheme up to the eighth order with respect to both space and time derivatives is presented. So far, in majority of publications this modified equation has been derived mainly as a fourth-order equation. The MDE is presented in the so-called Π-form of the first differential

Eddy-permitting numerical ocean models resolve mesoscale turbulence only partly, that leads to underestimation of eddy kinetic energy (EKE). Mesoscale dynamics can be amplified by using kinetic energy backscatter (KEB) parameterizations returning energy from the unresolved scales. We consider two types of KEB: stochastic and negative viscosity ones. The tuning of their amplitudes is based on a local

The paper is focused on problem of filtering random processes in dynamical systems whose mathematical models are described by stochastic differential equations with a Poisson component. The solution of a filtering problem supposes simulation of trajectories of solutions to a stochastic differential equation. The trajectory modelling procedure includes simulation of a Poisson flow permitting application