Logistic Fractional Variable-Order Equation - Numerical Simulations for Fitting Parameters

2018 ◽  
Author(s):  
Dorota Mozyrska ◽  
Piotr Oziablo
Keyword(s):  
Numerical Simulations ◽  
Order Equation ◽  
Variable Order ◽  
Fitting Parameters

Sub-regional event mixing constraints for two-pion Bose–Einstein correlations measurements in ππx system

2019 ◽  
Vol 28 (04) ◽  
pp. 1950024
Author(s):  
Q. He ◽  
T. Li ◽  
X. He ◽  
K. Zhuang
Keyword(s):  
Numerical Simulations ◽  
Systematic Bias ◽  
New Approach ◽  
Mixing Method ◽  
Bose Einstein ◽  
Fitting Parameters

Current BEC measurements in exclusive reactions with very low multiplicities is still a big challenge due to lack of effective observing method. Previously proposed observing approaches using event mixing technique still face problems of sample reduction and introducing extra and unnecessary fitting parameters. Here, we show the viability of a new event mixing approach with sub-regional mixing constraints related to energy hierarchy and energy sum observables. Extensive numerical simulations are performed to test the new mixing technique. Its ability to observe BEC parameters is validated and the systematic bias of the fit BEC parameter [Formula: see text] is improved since this new approach reduces the fitting parameters from 4 to 3 compared to the previously proposed mixing method.

scholarly journals An accurate approach based on the orthonormal shifted discrete Legendre polynomials for variable-order fractional Sobolev equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. H. Heydari ◽  
A. Atangana
Keyword(s):  
Legendre Polynomials ◽  
Algebraic System ◽  
Operational Matrix ◽  
Order Equation ◽  
Basis Functions ◽  
Variable Order ◽  
System Of Equations ◽  
Sobolev Equation ◽  
Numerical Examples ◽  
Operational Matrix Method

AbstractThis paper applies the Heydari–Hosseininia nonsingular fractional derivative for defining a variable-order fractional version of the Sobolev equation. The orthonormal shifted discrete Legendre polynomials, as an appropriate family of basis functions, are employed to generate an operational matrix method for this equation. A new fractional operational matrix related to these polynomials is extracted and employed to construct the presented method. Using this approach, an algebraic system of equations is obtained instead of the original variable-order equation. The numerical solution of this system can be found easily. Some numerical examples are provided for verifying the accuracy of the generated approach.

scholarly journals A New Measurement Method for High Voltages Applied to an Ion Trap Generated by an RF Resonator

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1143
Author(s):  
Yunjae Park ◽  
Changhyun Jung ◽  
Myeongseok Seong ◽  
Minjae Lee ◽  
Dongil Dan Cho ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Measurement Method ◽  
Ion Trap ◽  
Functional Relation ◽  
Voltage Divider ◽  
Ion Traps ◽  
Absolute Amplitude ◽  
Simulation Results ◽  
Rf Shielding ◽  
Fitting Parameters

A new method is proposed to measure unknown amplitudes of radio frequency (RF) voltages applied to ion traps, using a pre-calibrated voltage divider with RF shielding. In contrast to previous approaches that estimate the applied voltage by comparing the measured secular frequencies with a numerical simulation, we propose using a pre-calibrated voltage divider to determine the absolute amplitude of large RF voltages amplified by a helical resonator. The proposed method does not require measurement of secular frequencies and completely removes uncertainty caused by limitations of numerical simulations. To experimentally demonstrate our method, we first obtained a functional relation between measured secular frequencies and large amplitudes of RF voltages using the calibrated voltage divider. A comparison of measured relations and simulation results without any fitting parameters confirmed the validity of the proposed method. Our method can be applied to most ion trap experiments. In particular, it will be an essential tool for surface ion traps which are extremely vulnerable to unknown large RF voltages and for improving the accuracy of numerical simulations for ion trap experiments.

Evaluation of Two Mathematical Models Applied to Soybean Hydration

2010 ◽  
Vol 6 (6) ◽  
Author(s):  
Mônica Ronobo Coutinho ◽  
Edilson Sadayuki Omoto ◽  
Wagner André dos Santos Conceição ◽  
Cid Marcos Gonçalves Andrade ◽  
Luiz Mario Matos Jorge
Keyword(s):  
Order Differential Equation ◽  
Order Equation ◽  
Distributed Parameter ◽  
Fluid Interface ◽  
First Order ◽  
Differential Element ◽  
Quadratic Deviation ◽  
Diffusion And Convection ◽  
Simulation Results ◽  
Fitting Parameters

The predictions of the Hsu model of soybean hydration are compared with simulation results of the distributed parameter phenomenological model (DPP) that was developed in this study. The models were developed based on the same mass balance with one volume differential element of the Hsu model; however, the Hsu model admits an exponential variation of concentration while the DPP model admits equal diffusion and convection fluxes at the solid-fluid interface. The models are represented by a partial second order differential equation in relation to the radial position and a first order equation in relation to time, which were solved and numerically fitted using MATLAB routines and experimental data obtained from the hydration assays in the temperature range from 10 to 50 °C. The Hsu model has a smaller quadratic deviation; however, it employs three fitting parameters while DPP uses only one.

scholarly journals Some Aspects of Numerical Analysis for a Model Nonlinear Fractional Variable Order Equation

2021 ◽  
Vol 26 (3) ◽  
pp. 55
Author(s):  
Roman Parovik ◽  
Dmitriy Tverdyi
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Nonlinear Ordinary Differential Equation ◽  
Order Equation ◽  
Variable Order ◽  
Computational Accuracy ◽  
Order Of Accuracy ◽  
First Order ◽  
Explicit Finite Difference

The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of a nonlinear, ordinary differential equation with a derivative of a fractional variable order of the Gerasimov–Caputo type. The questions of approximation, convergence, and stability of this scheme are studied. It is shown that the nonlocal finite-difference scheme is conditionally stable and converges to the first order. Using the fractional Riccati equation as an example, the computational accuracy of the numerical method is analyzed. It is shown that with an increase in the nodes of the computational grid, the order of computational accuracy tends to unity, i.e., to the theoretical value of the order of accuracy.

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