A Fast Method for Fault Phase Selection Based on the Fitting Error of Transmission Line Differential Equation Algorithm

The differential equation describing the small signal behavior of a MOSFET channel is derived. Based on the analogy of the channel to distributed transmission lines, which has been very well established in literature, an entirely new RGC line model of MOSFET is presented. The element values of the line are determined by equivalence to a general distributed transmission line and subsequently the model is lumped into a single section in two possible Π and T representations. The postulated model considerably simplifies the study of the properties and behavior of MOSFET structures and can be suitably utilized in analysis and Computer Aided Design.

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Fast Calculation Method for Transient Response of Transmission Line Based on Chebyshev Pseudospectral–Two-Step Three-Order Boundary Value Coupled Method

Symmetry ◽

10.3390/sym11050721 ◽

2019 ◽

Vol 11 (5) ◽

pp. 721 ◽

Cited By ~ 1

Author(s):

Zhenhua Li ◽

Tinghe Hu ◽

Yuan Tao ◽

Tao Zhang ◽

Zhenxing Li

Keyword(s):

Differential Equation ◽

Transmission Line ◽

Transient Response ◽

Differential Quadrature Method ◽

Boundary Value ◽

Pseudospectral Method ◽

Telegraph Equation ◽

Space Domain ◽

Coupled Method ◽

Chebyshev Pseudospectral

A Chebyshev pseudospectral–two-step three-order boundary value coupled method is proposed and presented for handling the issue associated with complicated calculation, low precision, and poor stability in the process of transient response of transmission line. The first order differential equation in time domain is obtained via dispersing the telegraph equation in space domain by utilizing the pseudospectral method (PSM) based on Chebyshev polynomial. Then the two-step three-order boundary value method (BVM3) is presented and employed to resolve the obtained differential equation, so the numerical solution of the space discrete points can be obtained. Furthermore, the Chebyshev pseudospectral–two-step three-order boundary value coupled method (PSM-BVM3) is presented and compared with the Chebyshev pseudospectral–two-step two order boundary value coupled method (PSM-BVM2), the pseudospectral–differential quadrature method (PSM-DQM), and the pseudospectral method–trapezoid rule (PSM-TR) to validate the feasibility of the new proposed method. Theoretical analysis and numerical simulation reveal that the proposed Chebyshev PSM-BVM3 has a higher performance than the conventional method. For the proposed Chebyshev PSM-BVM3, the higher precision, efficiency, and numerical stability can be obtained and achieved only with fewer discrete points in the space domain, which is suitable for solving the transient response of transmission line. The proposed PSM-BVM3 can improve the drawback of numerical instability of the PSM and can also improve the disadvantage of the BVM as it is not easy to change the latter’s timestep size.

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A Fast Method for the Determination of Emergent Intensities in Radiative Transfer Theory

Publications of the Astronomical Society of Australia ◽

10.1017/s132335800001273x ◽

1971 ◽

Vol 2 (1) ◽

pp. 42-43 ◽

Cited By ~ 3

Author(s):

C. J. Cannon

Keyword(s):

Differential Equation ◽

Radiative Transfer ◽

Source Function ◽

Order Differential Equation ◽

Fast Method ◽

First Order ◽

Integration Schemes ◽

Emergent Intensity ◽

Difficult Part

One of the quantities usually required when solving the equation of radiative transfer is the intensity of radiation emerging from the surface of the medium under consideration. For multi-dimensional situations however, the methods presented to date have been numerical, and these first calculate the so-called source function Sv (r, Ω) as a function of position r, angle Ω and frequency v. This is generally the most difficult part of the exercise since an integro-difierential equation must be solved. The emergent intensity is then determined by solving a relatively simple first order differential equation by any of the well known numerical integration schemes. However, if the emergent intensity is required at a large number of angles, frequencies, and positions on the surface of the medium, and this is usually the case, the amount of computing needed may be considerable.

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