A novel method for determining fixed running time in operating electric train tracking optimal speed profile

<span lang="EN-US">Tracking the optimal speed profile in electric train operation has been proposed as a potential solution for reducing energy consumption in electric train operation, at no cost to improve infrastructure of existing Metro lines as well. However, the optimal speed profile needs to meet fixed running time. Therefore, this paper focuses on a new method for determining the fixed running time complied with the scheduled timetable when trains track the optimal speed profile. The novel method to ensure the fixed running time is the numerical-analytical one. Calculating accelerating time ta, coasting time tc, braking time tb via values of holding speed vh, braking speed vb of optimal speed profile with the constraint condition: the running time equal to the demand time. The other hands, vh and vb are determined by solving nonlinear equations with constraint conditions. Additionally, changing running time suit for each operation stage of metro lines or lines starting to conduct schedules by the numerical-analytical method is quite easy. Simulation results obtained for two scenarios with data collected from electrified trains of Cat Linh-Ha Dong metro line, Vietnam show that running time complied with scheduled timetables, energy saving by tracking optimal speed profile for the entire route is up to 8.7%, if the running time is one second longer than original time, energy saving is about 11.96%.</span>

Solving the problem of mathematical models overparameterization for some nonlinear oscillating systems

This study proposes a numerical-analytical method that allows us to simplify the model, which is obtained on the basis of the single observable variable of an object under the study, and which may be overparameterized. As a model, we consider a system of ordinary differential equations with polynomial right-hand sides. To solve this problem, the so-called differential model is used, that is, a system in which unknown variables are replaced by derivatives of the observed variable, and which is derived on the basis of a system under the study so that the observed variables of these systems coincide. The method of simplification of a system under the study is based on the fact that using a numerical method, a simpler differential model can be obtained. Next, an analytical transition from a simplified differential model to a simplified original system is performed. In this case, the time series error remains within given limits even for systems with deterministic chaos, despite their high sensitivity to the initial conditions.

Modelling the Temperature State of Bodies with Internal Heat Sources

This article presents the results of the development of a numerical - analytical method for solving the problem of thermal conductivity in a plate fuel element. An unsteady temperature field inside a fuel element is investigated for a given spatial distribution of heat sources. The heat release rate is given by the quadratic function of the coordinate. Modeling the temperature state of bodies with internal heat sources allows you to study the operation of equipment in transient modes, control heating/cooling modes of elements, determine temperature stresses, etc. It is shown in the work that regardless of the power of internal sources of heat, the temperature state is stabilized at a temperature level that depends on the Pomerantsev number.

DETERMINATION OF THE INHOMOGENEITY PARAMETERS OF A SPHERE’S COVER ENSURING REQUIRED SOUND REFLECTION IN A WAVEGUIDE

The numerical-analytical method of identifying the inhomogeneity parameters of a material of a sphere’s elastic cover, which allow to ensure minimal (maximal) average pressure in the scattered field of a spherical sound wave, which is radiated by a monopole source, within the disk observation domain in a cylindrical waveguide, has been developed. The sphere is assumed to be either absolutely rigid (moveless) or filled with an homogeneous elastic material. Verification of the scheme for determining the cover’s extremal inhomogeneity characteristics has been carried out and influence of the solution algorithm’s launch parameters on their identification accuracy during the numerical experiment has been evaluated. The finite element method (FEM) and the Hooke-Jeeves algorithm are used in the problem solving.

Numerical-analytical method for calculating the refraction of radio waves in a chaotic upper atmosphere

An operational method is proposed for calculating the refraction of decameter radio waves in a randomly-inhomogeneous upper atmosphere. The method is based on the numerical-analytical solution of stochastic equations of geometric optics. An integral expression is obtained for the dispersion of the refraction angle of a radio wave on the atmospheric path using the approximation of the perturbation method. For a quick calculation of the statistical moment of the refraction angle, the integral expression is reduced to an ordinary first-order differential equation. The joint numerical solution of the unperturbed ray equations and the equations for the statistical moment allows doing an operational estimate of beam width of radio waves arriving at the observation point. The results of numerical calculations of the standard deviations of the refraction angles of radio waves on paths of various lengths are presented.

PARALLEL COMPUTING MODEL WITH CONTINUOUS TIME

The aim of this work is to construct a numerical-analytical method of designing efficient algorithms for solution of tasks having the parabolic type. Using a priori information about the smoothness of solutions, great attention is paid to the construction of solutions of high -order accuracy. Creation of parallel computing systems required the development of mathematical concepts for constructing parallel algorithms, i.e. algorithms adapted for implementation in these systems. As the basis for constructing the parallel algorithm we can take both: a sequential algorithm and the task itself as well. The most sensible at parallelization of sequential algorithm is pragmatic approach; actually sequential algorithms detect common elements which further are transformed to a parallel form. It is shown, that the algorithm of numerical - analytical vectorization has the maximal parallel form and, hence, minimally possible time for realization on parallel computing devices.

Numerical-analytical method for solving boundary value problem for the generalized moisture transport equation

The paper studies qualitatively new equations of moisture transfer, which generalize the Aller and Aller-Lykov equations. The generalization contributes to revealing in the original equations the specific features of the studied massifs, their structure, physical properties, processes occurring in them through the introduction of the notion of the rates of change of the fractal dimension. We have obtained solutions to the constant coefficient difference equations as a system arising when using the method of lines for the equations with a Riemann-Liouville time fractional derivative with boundary conditions of the first kind. A priori estimates are obtained that imply convergence of the obtained solutions to systems of ordinary differential equations with variable fractional coefficients. Numerical tests have been carried out to confirm theoretical results of the study.