scholarly journals A New Approach for Approximate Solution of ADE: Physical-Based Modeling of Carriers in Doping Region

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 458
Author(s):  
Leobardo Hernandez-Gonzalez ◽  
Jazmin Ramirez-Hernandez ◽  
Oswaldo Ulises Juarez-Sandoval ◽  
Miguel Angel Olivares-Robles ◽  
Ramon Blanco Sanchez ◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytic Solution ◽  
Order Differential Equation ◽  
Electric Circuit ◽  
New Approach ◽  
In Doping ◽  
Electric Behavior ◽  
Spatio Temporal ◽  
Physical Phenomena

The electric behavior in semiconductor devices is the result of the electric carriers’ injection and evacuation in the low doping region, N-. The carrier’s dynamic is determined by the ambipolar diffusion equation (ADE), which involves the main physical phenomena in the low doping region. The ADE does not have a direct analytic solution since it is a spatio-temporal second-order differential equation. The numerical solution is the most used, but is inadequate to be integrated into commercial electric circuit simulators. In this paper, an empiric approximation is proposed as the solution of the ADE. The proposed solution was validated using the final equations that were implemented in a simulator; the results were compared with the experimental results in each phase, obtaining a similarity in the current waveforms. Finally, an advantage of the proposed methodology is that the final expressions obtained can be easily implemented in commercial simulators.

scholarly journals A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Alvaro H. Salas S ◽  
Jairo E. Castillo H ◽  
Darin J. Mosquera P
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytical Solution ◽  
Initial Conditions ◽  
Negative Ions ◽  
Nonlinear Problems ◽  
New Approach ◽  
Weierstrass Elliptic Function ◽  
Electronegative Plasma ◽  
The Given

In this paper, a new analytical solution to the undamped Helmholtz oscillator equation in terms of the Weierstrass elliptic function is reported. The solution is given for any arbitrary initial conditions. A comparison between our new solution and the numerical approximate solution using the Range Kutta approach is performed. We think that the methodology employed here may be useful in the study of several nonlinear problems described by a differential equation of the form z ″ = F z in the sense that z = z t . In this context, our solutions are applied to some physical applications such as the signal that can propagate in the LC series circuits. Also, these solutions were used to describe and investigate some oscillations in plasma physics such as oscillations in electronegative plasma with Maxwellian electrons and negative ions.

On Axisymmetric Vibration of Annular Plate of Parabolic Thickness Variation by Factorization of Differential Equation

2001 ◽  
Author(s):  
Dumitru I. Caruntu
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Analytic Solution ◽  
Order Differential Equation ◽  
Annular Plate ◽  
Poisson's Ratio ◽  
Thickness Variation ◽  
Axisymmetric Vibration ◽  
Annular Plates ◽  
Fourth Order Differential Equation

Abstract In the present paper an analytic solution of free axisymmetric vibration of a class of annular plates of parabolic thickness variation is obtained by factorization of the fourth-order differential equation. Poisson’s ratio is taken v = 1/3, applicable to many materials.

scholarly journals Analytic Solutions of a Second-Order Functional Differential Equation with a State Derivative Dependent Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Jiraphorn Somsuwan ◽  
Keaitsuda Maneeruk Nakprasit
Keyword(s):  
Differential Equation ◽  
Power Series ◽  
Analytic Solution ◽  
Order Differential Equation ◽  
Polynomial Solution ◽  
Analytic Solutions ◽  
Second Order ◽  
Auxiliary Equation ◽  
Convergent Power Series ◽  
Functional Differential

We investigate an analytic solution of the second-order differential equation with a state derivative dependent delay of the formx″(z)=x(p(z)+bx′(z)). Considering a convergent power seriesg(z)of an auxiliary equationγ2g″(γz)g′(z)=[g(γ2z)-p(g(γz))]γg′(γz)(g′(z))2+p′′(g(z))(g′(z))3+γg′(γz)g″(z)with the relationp(z)+bx′(z)=g(γg-1(z)), we obtain an analytic solutionx(z). Furthermore, we characterize a polynomial solution whenp(z)is a polynomial.

scholarly journals A New Approach for Solving the Complex Cubic-Quintic Duffing Oscillator Equation for Given Arbitrary Initial Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Alvaro H. Salas ◽  
Simeon Casanova Trujillo
Keyword(s):  
Differential Equation ◽  
Analytic Solution ◽  
Initial Conditions ◽  
Duffing Oscillator ◽  
Integrable Case ◽  
New Approach ◽  
One Dimensional ◽  
Weierstrass Elliptic Function ◽  
Quintic Equation ◽  
The One

The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly, providing exact expressions for the period and the solution. The period as well as the exact analytic solution is given in terms of the famous Weierstrass elliptic function. An integrable case of a damped cubic-quintic equation is presented. Mathematica code for solving both cubic and cubic-quintic Duffing equations is given in Appendix at the end.

Approximately Analytic Solution of the Differential Equation of Damped Odd Power Oscillator

2014 ◽  
Vol 488-489 ◽  
pp. 1185-1188
Author(s):  
Yuan Huang
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Nonlinear Oscillator ◽  
Analytic Solution ◽  
Averaging Method ◽  
Numerical Results ◽  
Power Oscillator

The approximately analytic solution of the differential equation of the damped vibration of the strongly odd power nonlinear oscillator has been obtained by harmonically averaging method. By comparing with numerical results, it is proven that the principle of the attenuation of amplitude gotten by this method is almost exact, and the approximate solution is valid.

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