scholarly journals Second Order Newton Iteration Method and Its Application to MOS Compact Modeling and Circuit Simulation

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 141-145 ◽  
Author(s):  
Zhiping Yu ◽  
Robert W. Dutton
Keyword(s):  
Circuit Simulation ◽  
Iteration Scheme ◽  
Newton Iteration ◽  
Initial Guess ◽  
Second Order ◽  
Compact Modeling ◽  
Algebraic Equations ◽  
Potential Applications ◽  
Pros And Cons ◽  
Newton Iteration Method

A robust second order Newton iteration scheme is proposed for solving the nonlinear algebraic equations. Potential applications include the projection of the initial guess to the solution when the parameters in the equations are changed. The mathematical derivation leading to the scheme is given and pros and cons of the method are discussed. As an example, the method has been applied to the evaluation of charge-sheet model for MOS as used in the circuit simulation.

scholarly journals A family of modified Newton iteration method for solving nonlinear algebraic equations

2017 ◽  
Vol 20 (K2) ◽  
pp. 34-41
Author(s):  
Luc Xuan Nghiem ◽  
Hieu Nhu Nguyen
Keyword(s):  
Iteration Method ◽  
Order Of Convergence ◽  
Approximate Solutions ◽  
Newton Iteration ◽  
Convergence Order ◽  
Correction Function ◽  
Algebraic Equations ◽  
Order Condition ◽  
Nonlinear Algebraic Equations ◽  
Newton Iteration Method

In this study, a modified Newton iteration version for solving nonlinear algebraic equations is formulated using a correction function derived from convergence order condition of iteration. If the second order of convergence is selected, we get a family of the modified Newton iteration method. Several forms of the correction function are proposed in checking the effectiveness and accuracy of the present iteration method. For illustration, approximate solutions of four examples of nonlinear algebraic equations are obtained and then compared with those obtained from the classical Newton iteration method.

scholarly journals FUNCTIONALS WITH VALUES IN THE NON‐ARCHIMEDEAN FIELD OF LAURENT SERIES AND THEIR APPLICATIONS TO THE EQUATIONS OF ELASTICITY THEORY. I

2002 ◽  
Vol 7 (2) ◽  
pp. 297-312
Author(s):  
M. Radyna
Keyword(s):  
Nonlinear System ◽  
Calculation Method ◽  
Laurent Series ◽  
Numerical Test ◽  
Generalized Solution ◽  
Newton Iteration ◽  
Algebraic Equations ◽  
Hopf Equation ◽  
Newton Iteration Method ◽  
Definition Of

Functionals with values in Non‐Archimedean field of Laurent series applied to the definition of generalized solution (in the form of soliton) of the Hopf equation. Calculation method for the profile of infinitely narrow soliton is proposed. Applying this method, calculations of profiles are reduced to the nonlinear system of algebraic equations in R n+1, n > 1. It is shown that there is a possibility to find out some of the solutions of this system using the Newton iteration method. Example and numerical test are considered.

An introduction to an ancient Chinese algorithm and its modification

2016 ◽  
Vol 26 (8) ◽  
pp. 2486-2491 ◽  
Author(s):  
Chun-Hui He
Keyword(s):  
Numerical Simulation ◽  
Iteration Method ◽  
Newton Iteration ◽  
Initial Guess ◽  
Second Century ◽  
Content Type ◽  
Newton's Iteration ◽  
Newton Iteration Method ◽  
The Ancient Chinese ◽  
Practical Implications

Purpose Every student knows Newton’s iteration method from a textbook, which is widely used in numerical simulation, what few may know is that its ancient Chinese partner, Ying Buzu Shu, in about second century BC has much advantages over Newton’s method. The purpose of this paper is to introduce the ancient Chinese algorithm and its modifications for numerical simulation. Design/methodology/approach An example is given to show that the ancient Chinese algorithm is insensitive to initial guess, while a fast convergence rate is predicted. Findings Two new algorithms, which are suitable for numerical simulation, are introduced by absorbing the advantages of the Newton iteration method and the ancient Chinese algorithm. Research limitations/implications This paper focuses on a single algebraic equation; however, it is easy to extend the theory to algebraic systems. Practical implications The Newton iteration method can be updated in numerical simulation. Originality/value The ancient Chinese algorithm is elucidated to have modern applications in various numerical methods.

scholarly journals Reliability-Aware SPICE Compatible Compact Modeling of IGZO Inverters on a Flexible Substrate

2021 ◽  
Vol 11 (11) ◽  
pp. 4838
Author(s):  
Je-Hyuk Kim ◽  
Youngjin Seo ◽  
Jun Tae Jang ◽  
Shinyoung Park ◽  
Dongyeon Kang ◽  
...  
Keyword(s):  
Flexible Electronics ◽  
Circuit Simulation ◽  
Flexible Substrate ◽  
Atomic Layer ◽  
Operating Conditions ◽  
Gate Insulator ◽  
Compact Modeling ◽  
Indium Gallium Zinc Oxide ◽  
Electrical Stress ◽  
Bending Radius

Accurate circuit simulation reflecting physical and electrical stress is of importance in indium gallium zinc oxide (IGZO)-based flexible electronics. In particular, appropriate modeling of threshold voltage (VT) changes in different bias and bending conditions is required for reliability-aware simulation in both device and circuit levels. Here, we present SPICE compatible compact modeling of IGZO transistors and inverters having an atomic layer deposition (ALD) Al2O3 gate insulator on a polyethylene terephthalate (PET) substrate. Specifically, the modeling was performed to predict the behavior of the circuit using stretched exponential function (SEF) in a bending radius of 10 mm and operating voltages ranging between 4 and 8 V. The simulation results of the IGZO circuits matched well with the measured values in various operating conditions. It is expected that the proposed method can be applied to process improvement or circuit design by predicting the direct current (DC) and alternating current (AC) responses of flexible IGZO circuits.

scholarly journals On the behaviour of the sup- and inf-convolutions of a function near the boundary

1996 ◽  
Vol 53 (3) ◽  
pp. 515-520
Author(s):  
Timothy R. Cranny
Keyword(s):  
Second Order ◽  
Boundary Potential ◽  
Potential Applications ◽  
Regularity Results

The study of nonclassical solutions for elliptic and parabolic PDE's often involves the use of regularisation processes such as the sup- and inf-convolutions. In this note we study the behaviour of these regularised functions near the boundary of the domain, and derive constraints on the appropriate second-order sub- and superdifferentials on and near the boundary. Potential applications to regularity results are also noted.

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