scholarly journals Substantiating parameters brake system of the tractor trailer

2021 ◽  
Vol 264 ◽  
pp. 04019
Author(s):  
Abdulaziz Shermukhamedov ◽  
Nurillo Ergashev ◽  
Abdukhamid Azizov
Keyword(s):  
Differential Equations ◽  
Experimental Studies ◽  
Brake System ◽  
Control Line ◽  
Pneumatic Drive ◽  
Order Accuracy ◽  
Euler’S Method ◽  
First Order ◽  
Runge Kutta Method ◽  
Dynamic Circuits

The article discusses substantiating the parameters brake system of a tractor-trailer (TT). The section offers a comparative analysis of theoretical and experimental studies of the TT brake drive and the parameters of its elements. Based on that, ordinary differential equations were solved by the Runge - Kutta method, the first-order accuracy (Euler's method). To solve partial differential equations, we used a modified Lax - Wendroff scheme. The results were obtained using the methods described above are theoretically very consistent with the triggering time ts = 0.47 s and the experimental value 0.46 s. Thus, the studying dynamic circuits of the pneumatic drive of TT brakes showed a high converging theoretical characteristic for a typical control line of a drive with an accelerating valve with experimental data, and the error was no more than 5%.

scholarly journals Unsplit complex frequency-shifted PML implementation using auxiliary differential equations for seismic wave modeling

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. T141-T154 ◽  
Author(s):  
Wei Zhang ◽  
Yang Shen
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Differential Equations ◽  
Seismic Wave ◽  
Numerical Scheme ◽  
Complex Frequency ◽  
Order Accuracy ◽  
First Order ◽  
Time Marching ◽  
Interior Domain

The complex-frequency-shifted perfectly matched layer (CFS-PML) technique can efficiently absorb near-grazing incident waves. In seismic wave modeling, CFS-PML has been implemented by the first-order-accuracy convolutional PML technique or second-order-accuracy recursive convolution PML technique. Both use different algorithms than the numerical scheme for the interior domain to update auxiliary memory variables in the PML and thus cannot be used directly with higher-order time-marching schemes. We work with an unsplit-field CFS-PML implementation using auxiliary differential equations (ADEs) to update the auxiliary memory variables. This ADE CFS-PML results in complete first-order differential equations. Thus, the numerical scheme for the interior domain can be used to solve ADE CFS-PML equations. We have implemented ADE CFS-PML in the finite-difference time-domain method and in anonstaggered-grid finite-difference method with the fourth-order Runge-Kutta scheme, demonstrating its straightforward implementation in different numerical time-marching schemes. We have also theoretically analyzed the role of the scalingfactor of CFS-PML; it transforms the PML to a transversely isotropic material, reducing the effective wave speed normal to the PML layer and bending the wavefront toward the normal direction of the PML layer. Our numerical tests indicate that the optimal value reduces the points per dominant wavelength at the outermost boundary to three, about half the value required by the numerical scheme. We also have found that the PML equations should be derived taking the free-surface boundary condition into account in finite-difference methods. Otherwise, the free surface in the PML layer causes instability or ineffective absorption of surface waves. Tests show that we can use a narrow-slice mesh with ADE CFS-PML to simulate full wave propagation efficiently in models with complex structure.

scholarly journals Analysis of dynamic circuits of contactless switching devices

2021 ◽  
Vol 2094 (2) ◽  
pp. 022072
Author(s):  
E Kh Abduraimov ◽  
D Kh Khalmanov ◽  
B A Nurmatov ◽  
M B Peysenov ◽  
N J Toirova
Keyword(s):  
Differential Equations ◽  
Computer Model ◽  
Nonlinear Dynamic ◽  
Experimental Studies ◽  
Euler Method ◽  
The State ◽  
Methods Of Analysis ◽  
Dynamic Circuits ◽  
Virtual Computer ◽  
Switching Devices

Abstract The main content of the study is the analysis of theoretical and virtual-experimental studies and methods of analysis of transients in semiconductor nonlinear dynamic circuits of contactless switching devices, presents transient graphs constructed using a virtual computer model. In addition, presents solutions of differential equations of the state of such circuits by the numerical Euler method.

scholarly journals A New Two Derivative FSAL Runge-Kutta Method of Order Five in Four Stages

2020 ◽  
Vol 17 (1) ◽  
pp. 0166
Author(s):  
Hussain Et al.
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Numerical Results ◽  
New Method ◽  
Kutta Method ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.

scholarly journals A COMPARATIVE EXPLORATION ON DIFFERENT NUMERICAL METHODS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

2020 ◽  
Vol 15 (12) ◽  
Author(s):  
Mohammad Asif Arefin
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Euler Method ◽  
Euler’S Method ◽  
Runge Kutta Method ◽  
Accuracy Level ◽  
Runge Kutta ◽  
Matlab Programming

In this paper, the initial value problem of Ordinary Differential Equations has been solved by using different Numerical Methods namely Euler’s method, Modified Euler method, and Runge-Kutta method. Here all of the three proposed methods have to be analyzed to determine the accuracy level of each method. By using MATLAB Programming language first we find out the approximate numerical solution of some ordinary differential equations and then to determine the accuracy level of the proposed methods we compare all these solutions with the exact solution. It is observed that numerical solutions are in good agreement with the exact solutions and numerical solutions become more accurate when taken step sizes are very much small. Lastly, the error of each proposed method is determined and represents them graphically which reveals the superiority among all the three methods. We fund that, among the proposed methods Runge-Kutta 4th order method gives the accurate result and minimum amount of error.

scholarly journals Software for the numerical solution of first-order partial differential equations

2019 ◽  
Vol 27 (1) ◽  
pp. 42-48
Author(s):  
Yaroslav Yu Kuziv
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Computer Algebra ◽  
Partial Differential ◽  
First Order ◽  
Modern Computer ◽  
Runge Kutta Method ◽  
The Media ◽  
Cauchy Method ◽  
Analytical Expressions

Partial differential equations of the first order, arising in applied problems of optics and optoelectronics, often contain coefficients that are not defined by a single analytical expression in the entire considered domain. For example, the eikonal equation contains the refractive index, which is described by various expressions depending on the optical properties of the media that fill the domain under consideration. This type of equations cannot be analysed by standard tools built into modern computer algebra systems, including Maple.The paper deals with the adaptation of the classical Cauchy method of integrating partial differential equations of the first order to the case when the coefficients of the equation are given by various analytical expressions in the subdomains G1, . . . , Gk , into which the considered domain is divided. In this case, it is assumed that these subdomains are specified by inequalities. This integration method is implemented as a Python program using the SymPy library. The characteristics are calculatednumerically using the Runge-Kutta method, but taking into account the change in the expressions for the coefficients of the equation when passing from one subdomain to another. The main functions of the program are described, including those that can be used to illustrate the Cauchy method. The verification was carried out by comparison with the results obtained in the Maple computer algebra system.

Sign in / Sign up

Export Citation Format

Share Document