New method of solution of the one-dimensional Schr�dinger equation

1991 ◽  
Vol 88 (3) ◽  
pp. 1010-1012 ◽  
Author(s):  
V. K. Ignatovich
Keyword(s):  
New Method ◽  
Dinger Equation ◽  
One Dimensional ◽  
Method Of Solution ◽  
The One

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

A SIMPLE METHOD TO CONSTRUCT LOCAL EQUILIBRIUM FUNCTION FOR LATTICE BOLTZMANN METHOD

2013 ◽  
Vol 24 (06) ◽  
pp. 1350038
Author(s):  
P. WANG ◽  
S. Q. ZHANG
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Local Equilibrium ◽  
New Method ◽  
Ratio Test ◽  
Simple Method ◽  
One Dimensional ◽  
Equilibrium Function ◽  
The One ◽  
Boltzmann Method

We have developed a simple method to construct local equilibrium function for lattice Boltzmann method (LBM). This new method can make LBM model satisfy compressible flow with a flexible specific-heat ratio. Test cases, including the one-dimensional Sod flow, one-dimensional Lax flow and thermal Couette flow are presented. Good results obtained using proposed new method, indicate that the proposed method is potentially capable of constructing of the local equilibrium function for LBM.

Calculation of linear detonation instability: one-dimensional instability of plane detonation

1990 ◽  
Vol 216 ◽  
pp. 103-132 ◽  
Author(s):  
H. I. Lee ◽  
D. S. Stewart
Keyword(s):  
Acoustic Radiation ◽  
Radiation Condition ◽  
Linear Instability ◽  
Arbitrary Parameter ◽  
Neutral Stability ◽  
One Dimensional ◽  
Method Of Solution ◽  
The Laplace Transform ◽  
Detonation Instability ◽  
The One

The detonation stability problem is studied by a normal mode approach which greatly simplifies the calculation of linear instability of detonation in contrast to the Laplace transform procedure used by Erpenbeck. The method of solution, for an arbitrary parameter set, is a shooting method which can be automated to generate easily the required information about instability. The condition on the perturbations applied at the end of the reaction zone is shown to be interpreted as either a boundedness condition or an acoustic radiation condition. Continuous and numerically exact neutral stability curves and boundaries are given as well as growth rates and eigenfunctions which are calculated for the first time. Our calculations include the Chapman–Jouguet (CJ) case which presents no special difficulty. We give representative results for our detonation model and summarize the one-dimensional stability behaviour in parameter space. Comparison with previous results for the neutral stability boundaries and approximations to the unstable discrete spectrum are given. Parametric studies of the unstable, discrete spectrum's dependence on the activation energy and the overdrive factor are given with the implications for interpreting the physical mechanism of instability observed in experiments. This first paper is restricted to the case of one-dimensional linear instability. Extensions to transverse disturbances will be treated in a sequel.

A new method of solution for one-dimensional quasi-neutral bounded plasmas

2010 ◽  
Vol 76 (3-4) ◽  
pp. 617-625 ◽  
Author(s):  
M. KAMRAN ◽  
S. KUHN
Keyword(s):  
Present Method ◽  
Analytic Solution ◽  
Ion Source ◽  
New Method ◽  
Ion Density ◽  
One Dimensional ◽  
Plasma Equation ◽  
Neutrality Condition ◽  
Bounded Plasma ◽  
Method Of Solution

AbstractA new method is proposed for calculating the potential distribution Φ(z) in a one-dimensional quasi-neutral bounded plasma; Φ(z) is assumed to satisfy a quasi-neutrality condition (plasma equation) of the form ni{Φ(z)} = ne(Φ), where the electron density ne is a given function of Φ and the ion density ni is expressed in terms of trajectory integrals of the ion kinetic equation. While previous methods relied on formally solving a global integral equation (Riemann, Phys. Plasmas, vol. 13, 2006, paper no. 013503; Kos et al., Phys. Plasmas, vol. 16, 2009, paper no. 093503), the present method is characterized by piecewise analytic solution of the plasma equation in reasonably small intervals of z. As a first concrete application, Φ(z) is found analytically through order z4 near the center of a collisionless Tonks–Langmuir discharge with a cold-ion source.

A New Method and Device for Temperature Measurement Using One-Dimensional Heat Equation

1994 ◽  
Author(s):  
Nicolae A. Damean
Keyword(s):  
Heat Equation ◽  
Temperature Measurement ◽  
Low Temperatures ◽  
Principal Component ◽  
The Other ◽  
New Method ◽  
Gradient Algorithm ◽  
One Dimensional ◽  
The One ◽  
The Mathematical Model

Abstract A new method and device for temperature measurement are presented. The method reduces the measurement of the unknown temperature to the solving of an optimal control problem, using a numerical computer. The device consists of a hardware part including some conventional transducers and a software one. The problem of temperature measurement, according to this method, is mathematically modelled by means of the one-dimensional heat equation, describing the heat transfer through the device. The principal component of the device is a rod. The variation of the temperature which is produced near one end of the rod is determined using some temperature measurements in the other end of the rod, the mathematical model and a type of gradient algorithm. This device works as an attenuator of high temperatures and as an amplifier of low temperatures.

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