scholarly journals Fast and Robust Parameter Estimation in the Application of Fuzzy Logistic Equations in Population Growth

MATEMATIKA ◽  
2019 ◽  
Vol 35 (2) ◽  
pp. 249-259
Author(s):  
Nor Atirah Izzah ◽  
Yeak Su Hoe ◽  
Normah Maan
Keyword(s):  
Parameter Estimation ◽  
Population Growth ◽  
Kutta Method ◽  
Growth Data ◽  
Logistic Equations ◽  
Runge Kutta Method ◽  
Robust Parameter ◽  
Runge Kutta ◽  
Fourth Order Method ◽  
Robust Parameter Estimation

In this paper, extended Runge-Kutta fourth order method for directly solving the fuzzy logistic problem is presented. The extended Runge-Kutta method has lower number of function evaluations, compared with the classical Runge-Kutta method. The numerical robustness of the method in parameter estimation is enhanced via error minimization in predicting growth rate and carrying capacity. The results of fuzzy logistic model with the estimated parameters have been compared with population growth data in Malaysia, which indicate that this method is more accurate that the data population. Numerical example is given to illustrate the efficiency of the proposed model. It is concluded that robust parameter estimation technique is efficient in modelling population growth.

scholarly journals ANALISIS DINAMIS MODEL MATEMATIKA PERTUMBUHAN JUMLAH MAHASISWA PROGRAM STUDI PENDIDIKAN MATEMATIKA STKIP PGRI PASURUAN

2018 ◽  
Vol 1 (October) ◽  
pp. 61-66
Author(s):  
Wahyuni Ningsih ◽  
Rif’atul Khusniah
Keyword(s):  
Stability Analysis ◽  
Mathematics Education ◽  
Population Growth ◽  
Dynamic Analysis ◽  
Equilibrium Point ◽  
Education Program ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Model Completion

Mathematical Models of population growth on the number of students, especially in the mathematics education program STKIP PGRI Pasuruan has been obtained. One of the purposes of this modeling was to find out the behavior of the model or system. To determine the behavior of the systems can be used dynamic analysis of the model. Therefore, a dynamic analysis of the growth model in the number of students, especially in the mathematics education program STKIP PGRI Pasuruan has been done in this article. The dynamic analysis that is used in this article is about a stability analysis around the equilibrium point of the model. Completion of the model using the Runge-Kutta method was simulated so that obtained a graphical completion of the model. Analytical and graphical systems stability analysis showed that the system was asymptotically unstable.   Model matematika pertumbuhan populasi pada jumlah mahasiswa, khususnya di program studi pendidikan matematika STKIP PGRI Pasuruan sudah didapatkan. Salah satu tujuan dilakukan pemodelan ini adalah untuk mengetahui perilaku dari model atau sistem. Untuk mengetahui perilaku sistem dapat digunakan analisis dinamis terhadap model. Oleh karena itu, pada artikel ini dilakukan analisis dinamis terhadap model pertumbuhan jumlah mahasiswa program studi pendidikan matematika STKIP PGRI Pasuruan. Analisis dinamis yang digunakan pada artikel ini berupa analisis kestabilan sistem di sekitar titik setimbang model. Penyelesaian model menggunakan metode Runge-Kutta yang di simulasikan sehingga diperoleh bentuk penyelesaian model secara grafik. Analisis kestabilan sistem secara analitik dan grafik menunjukkan bahwa sistem tidak stabil asimtotik.

scholarly journals The application of fuzzy logistic equations in population growth with parameter estimation via minimization

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Nor Atirah Izzah Zulkefli ◽  
Su Hoe Yeak ◽  
Normah Maan
Keyword(s):  
Parameter Estimation ◽  
Population Growth ◽  
Logistic Model ◽  
Growth Parameter ◽  
Logistic Equations ◽  
Estimated Parameters ◽  
Proposed Model ◽  
Minimization Technique ◽  
Fourth Order Method ◽  
Gradient Approach

This paper presents a numerical solution for the first order fuzzy logistic equations by extended Runge-Kutta fourth order method with estimated parameters. The parameters are estimated by minimization technique using conjugate gradient approach. Then, the fuzzy logistic model with the estimated parameters is used to fit the population growth in Malaysia. Numerical example is given to show the efficiency of the proposed model. Keywords: Fuzzy logistic equations, Population growth, Parameter estimation, Minimization technique

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.

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