scholarly journals The Mathematical Model and Numerical Solution of Instantaneous Availabilities for the Two-Unit Series Repairable System and Parallel Repairable System with Three States

2018 ◽  
Vol 8 (10) ◽  
pp. 1759 ◽  
Author(s):  
Yi Yang ◽  
Qianbin Li ◽  
Xuefeng Chen
Keyword(s):  
Mathematical Model ◽  
Markov Process ◽  
Numerical Solution ◽  
Renewal Process ◽  
Parallel System ◽  
Repairable System ◽  
Series System ◽  
Trapezoidal Formula ◽  
The Mathematical Model

This paper is aimed to obtain the instantaneous availabilities (IAs) for the two-unit series system and parallel system with three states. By the compound S i m p s o n formula and the compound trapezoidal formula, we get the numerical solution of IA for the two-unit series system with three states based on the renewal process. With four-order R u n g e - K u t t a formula, the numerical solution of IA for the two-unit parallel system with three states is obtained based on the Markov process.

scholarly journals Mathematical Modeling of Pollution Transfer in Open Channel

2019 ◽  
pp. 49-50
Author(s):  
Petro Martyniuk ◽  
Oksana Ostapchuk ◽  
Vitalii Nalyvaiko
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Solution ◽  
Boundary Problem ◽  
Water Flow ◽  
Numerical Experiments ◽  
Open Channel ◽  
Computational Algorithm ◽  
The Mathematical Model

The problem of pollution transfer by water flow in open channel was considered. The mathematical model of the problem was constructed. The numerical solution of the onedimensional boundary problem was obtained. The computational algorithm for solving the problem was programmed to implement. A series of numerical experiments with their further analysis was conducted.

Studi Perpindahan Panas Material pada Sistem Koordinat Segitiga

2017 ◽  
Vol 1 ◽  
pp. 114
Author(s):  
Imam Basuki ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
The Finite Difference Method ◽  
The Mathematical Model

<p class="Normal1"><strong><em>Abstract: </em></strong><em>Partial Differential Equations (PDP) Laplace equation can be applied to the heat conduction. Heat conduction is a process that if two materials or two-part temperature material is contacted with another it will pass heat transfer. Conduction of heat in a triangle shaped object has a mathematical model in Cartesian coordinates. However, to facilitate the calculation, the mathematical model of heat conduction is transformed into the coordinates of the triangle. PDP numerical solution of Laplace solved using the finite difference method. Simulations performed on a triangle with some angle values α and β</em></p><p class="Normal1"><strong><em> </em></strong></p><p class="Normal1"><strong><em>Keywords:</em></strong><em>  heat transfer, triangle coordinates system.</em></p><p class="Normal1"><em> </em></p><p class="Normal1"><strong>Abstrak</strong> Persamaan Diferensial Parsial (PDP) Laplace  dapat diaplikasikan pada persamaan konduksi panas. Konduksi panas adalah suatu proses yang jika dua materi atau dua bagian materi temperaturnya disentuhkan dengan yang lainnya maka akan terjadilah perpindahan panas. Konduksi panas pada benda berbentuk segitiga mempunyai model matematika dalam koordinat cartesius. Namun untuk memudahkan perhitungan, model matematika konduksi panas tersebut ditransformasikan ke dalam koordinat segitiga. Penyelesaian numerik dari PDP Laplace diselesaikan menggunakan metode beda hingga. Simulasi dilakukan pada segitiga dengan beberapa nilai sudut  dan  </p><p class="Normal1"><strong> </strong></p><p class="Normal1"><strong>Kata kunci :</strong> perpindahan panas, sistem koordinat segitiga.</p>

THE APPLICA TION OF "FROZEN WALL " SOFTWARE IN SIMULA TION OF ARTIFICIAL GROUND FREEZING

2019 ◽  
Vol 4 (1) ◽  
pp. 269-282
Author(s):  
L.Y. Levin ◽  
◽  
M.A. Semin ◽  
A.V. Bogomyagkov ◽  
O.S. Parshakov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
General Information ◽  
Software Application ◽  
Ground Freezing ◽  
Artificial Ground Freezing ◽  
Frozen Wall ◽  
The Mathematical Model ◽  
Best Fit ◽  
Technical Measures

The paper presents general information about the software application “Frozen Wall ”, which was designed to simulate frozen wall formation around constructed vertical shafts. The main feature of the developed application is the possibility of calibrating the mathematical model for the best fit with the experimental temperature measurements by numerical solution of the inverse Stefan problem. In addition, it takes into account a number of technological processes that affect the state of the frozen wall. Based on calculations performed in the application, it is possible to develop technical measures aimed at ensuring the efficiency of mine shafts construction in difficult hydrogeological conditions.

New Method for Static Analysis of Frame Structures Considered Floor Deformation

2014 ◽  
Vol 501-504 ◽  
pp. 518-522
Author(s):  
Hua Zhang ◽  
Li Huang
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
State Space ◽  
Static Analysis ◽  
Frame Structure ◽  
Frame Structures ◽  
Internal Forces ◽  
State Method ◽  
The Mathematical Model ◽  
Computation Work

The piecewise continuum technique was used for the frame structure and a series-parallel system was taken for the mathematical model for the structure in which the deformation of floor slab had to be considered, and its state space equations were derived. Then the numerical solution of deformations and internal forces were obtained by using of state method. It is shown that the method of this paper has the advantages of less computation work and high precision.

scholarly journals A numerical solution by alternative Legendre polynomials on a model for novel coronavirus (COVID-19)

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Elham Hashemizadeh ◽  
Mohammad Ali Ebadi
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
Legendre Polynomials ◽  
Algebraic System ◽  
The Novel ◽  
Kutta Method ◽  
System Of Differential Equations ◽  
Runge Kutta Method ◽  
Novel Coronavirus ◽  
The Mathematical Model

Abstract Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus. This paper provides a numerical solution for the mathematical model of the novel coronavirus by the application of alternative Legendre polynomials to find the transmissibility of COVID-19. The mathematical model of the present problem is a system of differential equations. The goal is to convert this system to an algebraic system by use of the useful property of alternative Legendre polynomials and collocation method that can be solved easily. We compare the results of this method with those of the Runge–Kutta method to show the efficiency of the proposed method.

Numerical Solution of Pressure Underground Seepage Flow Using a Technique of Curvilinear Boundary-Fitted Coordinates

2014 ◽  
Vol 501-504 ◽  
pp. 1878-1882
Author(s):  
Hong Zhao ◽  
Wen Li Wei
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
Seepage Flow ◽  
Matrix Equations ◽  
The Finite Element Method ◽  
Curvilinear Boundary ◽  
Seepage Flows ◽  
Large Matrix ◽  
Physical Laws ◽  
The Mathematical Model

The technique of curvilinear boundary-fitted coordinate system is used for the mathematical model of pressure underground seepage flow and the boundary conditions and the method of solving the transformed equations have been presented. The computing example shows that the computed hydraulic parameters conform to the physical laws. Compared with the finite element method, the presented method need not solve the large matrix equations, and the computer memories and the time for computing are less. The mathematical model is effective for numerical solution of pressure underground seepage flows with complicated boundaries, and can be used in practice hydraulic engineering. Keywords-curvilinear boundary-fitted coordinate, pressure underground seepage flow, mathematical model

scholarly journals Mathematical Modelling of Mass Transfer in Zones of Complete and Incomplete Saturation under the Action of Systematic Combined Drainage

2019 ◽  
pp. 86-87
Author(s):  
Anatolii Vlasyuk ◽  
Tatiana Tsvietkova
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Porous Media ◽  
Boundary Value Problem ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Finite Differences ◽  
Unsaturated Porous Media ◽  
Vertical Drains ◽  
The Mathematical Model

The mathematical model of a processes mass transfer in saturated and unsaturated porous media to the filtertrap in isothermal conditions to the system of vertical drains is presented. The numerical solution of the respective boundary value problem was obtained by the method of finite differences using the numerical method of conformal mappings in an inverse statement.

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