International Journal of Mathematics and Physics

ISSN

2218-7987

2409-5508

Издатель

Al-Farabi Kazakh National University

Ключевые слова

Differential Equation...

Computational Fluid D...

Nonlinear Differentia...

Numerical methods in ...

Quantum Chromodynamic...

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Comparing the efficiency of GPU and CPU in gravitational lensing simulation
(Al-Farabi Kazakh National University, 2024-06-20)
Nurzada Beissen
;
Daniya Utepova
;
Vladimir N. Kossov
;
Saken Toktarbay
;
Manas Khassanov
In this study, we investigate the computational advancements in simulating gravitational lensing, particularly focusing on the Schwarzschild black hole model. The traditional approach of back ray tracing, where photons are traced back from the observer to the source, is computationally intensive, especially when aiming to achieve high-resolution images of lensing effects around black holes. By employing a numerical method that integrates the Schwarzschild metric with initial conditions derived from the observer's plane, we map the deflection of light around a black hole to generate simulated images of gravitational lensing.The core of our study is the comparison between traditional CPU-based computations and GPU-accelerated processes using the Numba library. Our findings reveal that GPU acceleration, with its parallel processing capabilities, significantly reduces computation time, particularly as the complexity of the simulation increases with larger grid sizes. This computational efficiency is crucial for simulations of gravitational lensing, where the number of independent calculations grows exponentially with the resolution and accuracy of the desired image.Our research underscores the importance of leveraging GPU technology for astrophysical simulations, offering a substantial improvement in performance over CPU-based methods. Keywords: Gravitational Lensing, GPU Parallelization, Schwarzschild Black Hole, Ray Tracing Methods, Numba Library.
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Numerical solution of a control problem for ordinary differential equations with multipoint integral condition
(Al-Farabi Kazakh National University, 2019-12-20)
A. T. Assanova
;
E. А. Bakirova
;
Zh. М. Каdirbayeva
A linear boundary value problem with a parameter for ordinary differential equations with multipoint integral conditionis investigated.The method of parameterization is used for solving the considered problem. The linear boundary value problem with a parameter for ordinary differential equations with multipoint integral condition by introducing additional parameters at the partition points is reduced to equivalent boundary value problem with parameters. The equivalent boundary value problem with parameters consists of the Cauchy problem for the system of ordinary differential equations with parameters, multipoint integral condition and continuity conditions. The solution of the Cauchy problem for the system of ordinary differential equations with parameters is constructed using the fundamental matrix of differential equation. The system of linear algebraic equations with respect to the parameters are composed by substituting the values of the corresponding points in the built solutions to the multipoint integral condition and the continuity condition. Numerical method for finding solution of the problem is suggested, which based on the solving the constructed system and Runge-Kutta method of the 4-th order for solving Cauchy problem on the subintervals.
Цитирования (OpenAlex) 6Цитирования (OpenCitations) 2
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Definition of aerodynamic characteristics wind turbine to Darrieus of system troposcino
(Al-Farabi Kazakh National University, 2016-01-01)
Sh. A. Ershin
;
A.K. Yershina
;
Rustem Manatbayev
;
A. K. Tulepbergenov
Recently the majority show interest in connection with a number of merits to vertically-axial wind turbine type to Darrieus. It is possible to tell that age such wind energy installations of 25-30 years whereas others types wind turbine (sailing, propeller) have seriously started to study almost 1,5 centuries. The theory of these wind turbine with sufficient completeness are resulted in known E. M.Fateyev's monograph. In the present to article results of a theoretical substantiation for one of design kinds wind turbine are stated Darrieus - systems troposcino. This constructive form of the device to Darrieus becomes more and more popular. The general theory is constructed, almost all constructive and aerodynamic characteristics (linear speed, carrying power, front resistance are defined; wind power operating ratio; the moment of rotation of the turbine ) this device. Thus, attempt to put basic bases of the theory of devices to Darrieus of system troposcino is made. This report shows main theoretical principles of troposkino wind-turbine. Theoretically were determined dynamical characteristics of the wind-turbine, such as: rotation moment, power, useful wind energy coefficient and physical model of the plant. The theoretical results were compared with well-known experimental data.
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A novel numerical implementation for solving problem for loaded DEPCAG
(Al-Farabi Kazakh National University, 2023-01-10)
Zh. М. Каdirbayeva
;
Roza E. Uteshova
;
G. Marat
;
B. B. Мinglibayeva
In this work, we propose a new computational approach is implemented to solve a two-point BVP for a loaded differential equation with piecewise constant argument of generalized type (DEPCAG) based on the Dzhumabaev parameterization method. In this method, as parameters, we take the values of the desired solution at the partition points which are chosen taking into account the specifics of the equation. The problem under consideration reduces to an equivalent parametric problem for ordinary differential equations. A solution to this problem, which in turn are found from a system of linear algebraic equations. The found values of the parameters are used to determine the values of the unknown function at the remaining points of the interval by solving auxiliary initial-value problems. We develop a novel numerical implementation for solving the considered a two-point BVP for loaded DEPCAG and provide two examples illustrating its application, where Mathcad software will be used for the calculation.
Цитирования (OpenAlex) 8Цитирования (OpenCitations) 7
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A shadows from the static black hole mimickers
(Al-Farabi Kazakh National University, 2023-01-10)
Aray Muratkhan
;
Ayazhan Orazymbet
;
Madina Zhakipova
;
M. Assylbek
;
Saken Toktarbay
In this work, we study shadows from the naked singularity spacetime. The most analytical solutions of black hole shadows only investigated the case that the geodesic equations for photons can separate variables. We review the spherical null naked singularity metric and this spherically symmetric naked singularity spacetime metric is the solution of Einstein equations with an anisotropic fluid source which has no photon sphere. We also review a static, axially-symmetric singular solution of the vacuum Einstein’s equations without an event horizon which is can be used to describe the exterior gravitational field of a mass distribution with quadrupole moment. Moreover, the corresponding spacetime is characterized by the presence of naked singularities. It is theoretically known that not only a black hole can cast shadow, but other compact objects such as naked singularities, gravastar or boson stars can also cast shadows. We present the analytical calculation of shadows for both naked singularities spacetime and compare with the shadow of Schwarzschild static black hole, we show that this can serve as a black hole mimicker. Keywords: compact object, naked singularity, shadow.
Цитирования (OpenAlex) 5

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