Runge–Kutta analysis for optimizing the Zn-catalyzed transesterification conditions of MA and MMA with diols to maximize monoesterified products

2021 ◽  
Author(s):  
Taito Kato ◽  
Shin-ya Akebi ◽  
Haruki Nagae ◽  
Koji Yonehara ◽  
Tomoharu Oku ◽  
...  
Keyword(s):  
Equilibrium State ◽  
Curve Fitting ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Curve Fitting Analysis ◽  
Runge Kutta

Terminal hydroxylated acrylate derivatives were prepared by transesterification using zinc catalyst. The time to reach the equilibrium state was analyzed by curve-fitting analysis based on the Runge–Kutta method for optimizing the best conditions.

Research on Badminton Flight Tracks Based on Aerodynamics

2013 ◽  
Vol 443 ◽  
pp. 180-183
Author(s):  
Wan Zhong Fu
Keyword(s):  
Curve Fitting ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
The World ◽  
Runge Kutta

Badminton is one of the popular sports in the world. Our country is located on the top of the world badminton list. In order to improve the player skills, we have made the following research. We have analyzed the design and the flight track of the badmintons in accordance with the aerodynamics and then establish a model. According to the hydromechanics, the stress the badminton takes when flying is analyzed, then the relation between resistance and the speed can be got. After the curve fitting, the curve fitting figure is shown to us. Finally, we simulate the badminton flight track by using Runge-Kutta method and then get the track figure.

Application of the piecewise constant method in nonlinear dynamics of drill string

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Yi Zhou ◽  
Lin Yang ◽  
Changyue Fan ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Drill String ◽  
Vibration Velocity ◽  
Kutta Method ◽  
Time Step ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

scholarly journals Randomized Runge–Kutta method — Stability and convergence under inexact information

2021 ◽  
pp. 101554
Author(s):  
Tomasz Bochacik ◽  
Maciej Goćwin ◽  
Paweł M. Morkisz ◽  
Paweł Przybyłowicz
Keyword(s):  
Stability And Convergence ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Inexact Information ◽  
Runge Kutta
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