scholarly journals A novel analytical solution of the deformed Doppler broadening function using the Kaniadakis distribution and the comparison of computational efficiencies with the numerical solution

2021 ◽  
Author(s):  
Willian V. de Abreu ◽  
Aquilino S. Martinez ◽  
Eduardo D. do Carmo ◽  
Alessandro C. Gonçalves
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Doppler Broadening

scholarly journals Analytical and Experimental Analyses of Nonlinear Vibrations in a Rotary Inverted Pendulum

2021 ◽  
Author(s):  
Mohammadjavad Rahimi dolatabad ◽  
Abdolreza Pasharavesh ◽  
Amir Ali Akbar Khayyat
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Closed Loop ◽  
Inverted Pendulum ◽  
Multiple Scales ◽  
Nonlinear Oscillations ◽  
Wide Frequency Range ◽  
Perturbative Method ◽  
Full State Feedback ◽  
Rotary Inverted Pendulum

Abstract Gaining insight into possible vibratory responses of dynamical systems around their stable equilibria is an essential step, which must be taken before their design and application. The results of such a study can significantly help prevent instability in closed-loop stabilized systems through avoiding the excitation of the system in the neighborhood of its resonance. This paper investigates nonlinear oscillations of a Rotary Inverted Pendulum (RIP) with a full-state feedback controller. Lagrange’s equations are employed to derive an accurate 2-DoF mathematical model, whose parameter values are extracted by both the measurement and 3D modeling of the real system components. Although the governing equations of a 2-DoF nonlinear system are difficult to solve, performing an analytical solution is of great importance, mostly because, compared to the numerical solution, the analytical solution can function as an accurate pattern. Additionally, the analytical solution is generally more appealing to engineers because their computational costs are less than those of the numerical solution. In this study, the perturbative method of multiple scales is used to obtain an analytical solution to the coupled nonlinear motion equations of the closed-loop system. Moreover, the parameters of the controller are determined, using the results of this solution. The findings reveal the existence of hardening- and softening-type resonances at the first and second vibrational modes, respectively. This led to a wide frequency range with moderately large-amplitude vibrations, which must be avoided when adjusting a time-varying set-point for the system. The analytical results of the nonlinear vibration of the RIP are verified by experimental measurements, and a very good agreement is observed between the results of both approaches.

scholarly journals Comparative Study of Analytic Solution and Numerical Solution of Baseband Symbol Signal Based on Optimal Generic Function

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Mingxin Liu ◽  
Wei Xue ◽  
Sergey B. Makarov ◽  
Junwei Qi ◽  
Beiming Li
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Solution Process ◽  
Development Trend ◽  
Partial Solution ◽  
Research Process ◽  
Constraint Condition ◽  
Energy Limit ◽  
Function Model ◽  
Boundary Constraints

In this paper, the optimal mathematical generic function model is established using the minimum out-of-band energy radiation criterion. Firstly, the energy limit conditions, boundary constraints, and peak-to-average ratio constraints are applied to the generic function model; thus, the analytical solutions are obtained under different parameters. Secondly, a single symbol signal energy constraint condition and boundary constraint condition are added to the generic function model; thus, the numerical solution of the different parameters is obtained. In the process of solving the analytical solution, the partial solution process is simplified to solve the analytical solution, and there are also digital truncation problems. In addition, the corresponding order of the Lagrange differential equation increases by a multiple of 2 when the parameter n increases, which makes the solution extremely complicated or even impossible to solve. The numerical solution is in line with the current development trend of digital communication, and there is no need to simplify the solution process in the process of solving the numerical solution. When the parameter n and the Fourier series m take different values, the obtained symbol signals can also meet the needs of different communication occasions. The relevant data of the above research process were solved by a MATLAB software simulation, which proves the correctness of the method and the superiority of the numerical method.

scholarly journals Transforming Arithmetic Asian Option PDE to the Parabolic Equation with Constant Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Zieneb Ali Elshegmani ◽  
Rokiah Rozita Ahmad ◽  
Saiful Hafiza Jaaman ◽  
Roza Hazli Zakaria
Keyword(s):  
Parabolic Equation ◽  
Analytical Solution ◽  
Heat Equation ◽  
Numerical Solution ◽  
Closed Form ◽  
Asian Option ◽  
Asian Options ◽  
New Approach ◽  
Constant Coefficients ◽  
Closed Form Analytical Solution

Arithmetic Asian options are difficult to price and hedge, since at present, there is no closed-form analytical solution to price them. Transforming the PDE of the arithmetic the Asian option to a heat equation with constant coefficients is found to be difficult or impossible. Also, the numerical solution of the arithmetic Asian option PDE is not very accurate since the Asian option has low volatility level. In this paper, we analyze the value of the arithmetic Asian option with a new approach using means of partial differential equations (PDEs), and we transform the PDE to a parabolic equation with constant coefficients. It has been shown previously that the PDE of the arithmetic Asian option cannot be transformed to a heat equation with constant coefficients. We, however, approach the problem and obtain the analytical solution of the arithmetic Asian option PDE.

An Integral Equation Method for Predicting Acoustic Emission within Enclosures

1985 ◽  
Vol 199 (2) ◽  
pp. 133-137 ◽  
Author(s):  
D T I Francis ◽  
M M Sadek
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Acoustic Emission ◽  
Analytical Solution ◽  
Numerical Solution ◽  
Finite Element Methods ◽  
Exact Analytical Solution ◽  
Integral Equation Method ◽  
Absorption Characteristics ◽  
Good Agreement

A method is presented for calculating the acoustic emission of a vibrating body within an enclosure whose surface has known absorption characteristics. It is based on a numerical solution of the Helmholtz integral equation. Solutions are given for the case of a pulsating sphere within a sphere, and good agreement with the exact analytical solution is reported. The method is of value for small and medium scale problems at lower frequencies, where traditional techniques are less reliable. It is also potentially less demanding computationally than finite element methods.

scholarly journals A Semi-Analytical Solution of Thick Truncated Cones Using Matched Asymptotic Method and Disk Form Multilayers

2014 ◽  
Vol 61 (3) ◽  
pp. 495-513 ◽  
Author(s):  
Mohammad Zamani Nejad ◽  
Mehdi Jabbari ◽  
Mehdi Ghannad
Keyword(s):  
Finite Element Method ◽  
Shear Stress ◽  
Analytical Solution ◽  
Differential Equations ◽  
Numerical Solution ◽  
Asymptotic Method ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
The Finite Element Method ◽  
Truncated Cone

Abstract In this article, the thick truncated cone shell is divided into disk-layers form with their thickness corresponding to the thickness of the cone. Due to the existence of shear stress in the truncated cone, the equations governing disk layers are obtained based on first shear deformation theory. These equations are in the form of a set of general differential equations. Given that the truncated cone is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. The results obtained have been compared with those obtained through the analytical solution and the numerical solution. For the purpose of the analytical solution, use has been made of matched asymptotic method (MAM) and for the numerical solution, the finite element method (FEM).

scholarly journals Computational Sinc-scheme for extracting analytical solution for the model Kuramoto-Sivashinsky equation

2019 ◽  
Vol 9 (5) ◽  
pp. 3720
Author(s):  
Kamel Al-Khaled ◽  
Issam Abu-Irwaq
Keyword(s):  
Analytical Solution ◽  
Galerkin Method ◽  
Numerical Solution ◽  
Present Article ◽  
Point Theory ◽  
Algebraic Equations ◽  
Time Direction ◽  
Numerical Examples ◽  
Sivashinsky Equation ◽  
Crank Nicolson

The present article is designed to supply two different numerical<br />solutions for solving  Kuramoto-Sivashinsky equation. We have made<br />an attempt to develop a numerical solution via the use of<br />Sinc-Galerkin method for  Kuramoto-Sivashinsky equation, Sinc<br />approximations to both derivatives and indefinite integrals reduce<br />the solution to an explicit system of algebraic equations. The fixed<br />point theory is used to prove the convergence of the proposed<br />methods. For comparison purposes, a combination of a Crank-Nicolson<br />formula in the time direction, with the Sinc-collocation in the<br />space direction is presented, where the derivatives in the space<br />variable are replaced by the necessary matrices to produce a system<br />of algebraic equations. In addition, we present numerical examples<br />and comparisons to support the validity of these proposed<br />methods.

scholarly journals Analytical solution of Buckley-Leverett equation for gas flooding including the effect of miscibility with constant-pressure boundary

2019 ◽  
Vol 37 (3) ◽  
pp. 960-991 ◽  
Author(s):  
Lingyu Mu ◽  
Xinwei Liao ◽  
Zhiming Chen ◽  
Jiandong Zou ◽  
Hongyang Chu ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Relative Permeability ◽  
Constant Pressure ◽  
Gas Production ◽  
Influential Factors ◽  
Fractional Flow ◽  
Pressure Profiles ◽  
Gas Flooding ◽  
Volumetric Flux

This paper presents an analytical solution of Buckley-Leverett equation for gas flooding with constant-pressure boundary including the effect of miscibility on the viscosity and relative permeability. First, a relative permeability model and a viscosity model with consideration of miscibility are used to describe the variations of relative permeability and viscosity of oil and gas. Then, based on the fractional-flow theory, the Buckley-Leverett equation for gas flooding with constant-pressure boundary including the effect of miscibility is constructed and solved analytically. From the analytical solution, the saturation and pressure profiles, the total volumetric flux and the breakthrough time are determined. To verify the theory, the analytical solution is compared with the numerical solution. The comparison shows that the analytical solution is in reasonable agreement with numerical solution. Through the study on the influential factors, it can be concluded that total volumetric flux is increasing with the increases of permeability and pressure and decrease of gas viscosity. The increase of total volumetric flux accelerates breakthrough of the injected gas. Furthermore, with the pressure increase, there are remarkable reduction in residual oil saturation and improvement of relative permeability, resulting in higher gas saturation and oil displacement efficiency. The analytical solution presented in this paper provides guidance on analyzing the distribution of saturation and pressure profiles, predicting the gas production and oil recovery efficiency of oil well.

scholarly journals Stability Analysis of One-Leg Methods for Nonlinear Neutral Delay Integrodifferential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yuexin Yu ◽  
Liping Wen
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Analytical Solution ◽  
Global Stability ◽  
Numerical Solution ◽  
Integrodifferential Equations ◽  
Neutral Delay ◽  
Numerical Tests ◽  
Theoretical Results

This paper is concerned with the numerical solution of nonlinear neutral delay integrodifferential equations (NDIDEs). The adaptation of one-leg methods is considered. It is proved that anA-stable one-leg method can preserve the global stability and a stronglyA-stable one-leg method can preserve the asymptotic stability of the analytical solution of nonlinear NDIDEs. Numerical tests are given to confirm the theoretical results.

scholarly journals The Positivity of Numerical Method for Susceptible-Infected-Recovered-Susceptible Epidemic Model

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Feng Feng ◽  
Zong Wang
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Numerical Method ◽  
Epidemic Model ◽  
Numerical Technique ◽  
Environmental Perturbations ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Balanced Implicit Method ◽  
Stochastic Sirs Epidemic Model

Sudden environmental perturbations may affect the positivity of the solution of the susceptible-infected-recovered-susceptible (SIRS) model. Most of the SIRS epidemic models have no analytical solution. Thus, in order to find the appropriate solution, the numerical technique becomes more essential for us to solve the dynamic behavior of epidemics. In this paper, we are concerned with the positivity of the numerical solution of a stochastic SIRS epidemic model. A new numerical method that is the balanced implicit method (BIM) is set, which preserves the positivity under given conditions. The BIM method can maintain positive numerical solution. An illustrative numerical instance is presented for the numerical BIM of the stochastic SIRS model.

scholarly journals A Concise Method for Analyzing the Ice-Melting Performance of a Heated Disc

1976 ◽  
Vol 17 (76) ◽  
pp. 355-358
Author(s):  
J.F. Lea
Keyword(s):  
Analytical Solution ◽  
Temperature Dependence ◽  
Numerical Solution ◽  
Ice Melting ◽  
Numerical Work ◽  
Fluid Properties ◽  
Heated Disc ◽  
Special Case

AbstractShreve (1962) evaluated the performance of solid-nose hotpoints of various geometries. A more concise method for analysis of the special case of a flat disc melting into ice is presented here. In contrast to the numerical solution presented by Shreve, this method results in a closed analytical solution, based on constant properties, which is corrected using a property ratio scheme. This technique allows the substitution of various fluid properties into the solutions as might be required when considering contaminated or saline ice or other liquids. Shreve's method would require some additional numerical work to evaluate various properties because the temperature dependence of the viscosity of water is integrated into the results.Results obtained for the flat disc using this method are shown to compare favorably with Shreve's, indicating that this type of analysis may be applicable to other melt-unit geometries.

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