Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

scholarly journals Stability of the Difference Schemes for the Equations of Weakly Compressible Liquid

2007 ◽  
Vol 7 (3) ◽  
pp. 208-220 ◽  
Author(s):  
P. Matus ◽  
O. Korolyova ◽  
M. Chuiko
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Initial Conditions ◽  
Compressible Liquid ◽  
Stability Conditions ◽  
Differential Problem ◽  
Weakly Compressible ◽  
Linear Problems ◽  
The Difference ◽  
The Stability

Abstract A priory estimates of the stability in the sense of the initial data of the difference scheme approximating weakly compressible liquid equations in the Riemann invariants have been obtained. These estimates have been proved without any assumptions about the properties of the solution of the differential problem and depend only on the behavior of the initial conditions. As distinct from linear problems, the obtained estimates of stability in the general case exist only for a finite instant of time t≤t_0. In particular, this is confirmed by the fact, that nonfulfilment of these stability conditions lead to the appearance of supersonic flows or domains with large gradients. The questions of uniqueness and convergence of the difference solution are considered also. The results of the computating experiment confirming the theoretical conclusions are given.

scholarly journals COEFFICIENT STABILITY OF OPERATOR‐DIFFERENCE SCHEMES WITH TIME VARIABLE OPERATORS

1998 ◽  
Vol 3 (1) ◽  
pp. 152-159
Author(s):  
I. N. Panayotova
Keyword(s):  
Differential Operator ◽  
Initial Data ◽  
A Priori ◽  
Time Variable ◽  
Energy Space ◽  
Difference Schemes ◽  
Operator Equations ◽  
Variable Operator ◽  
The Right ◽  
Coefficient Stability

The problem of the coefficient stability for operator‐ difference schemes with variable operator is investigated. A priori coordinated estimates in the L 2‐norm are obtained for differential‐operator equations and operator‐difference schemes. Estimates in the energy space HA for coefficient stability and stability with respect to the right-hand side and the initial data are proved under more strong assumptions for operator's perturbation.

scholarly journals THE STABILITY CONDITIONS OF FINITE DIFFERENCE SCHEMES FOR SCHRÖDINGER, KURAMOTO‐TSZUKI AND HEAT EQUATIONS

1998 ◽  
Vol 3 (1) ◽  
pp. 177-194 ◽  
Author(s):  
M. Radžiūnas ◽  
F. Ivanauskas
Keyword(s):  
Finite Difference ◽  
Initial Boundary ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Heat Equations ◽  
Initial Boundary Value Problems ◽  
L2 Norm ◽  
The Stability ◽  
Conditions Of Stability ◽  
Initial Boundary Value

We consider various finite difference schemes for the first and the second initial‐boundary value problems for linear Kuramoto‐Tsuzuki, heat and Schrödinger equations in d‐dimensional case. Using spectral methods, we find the conditions of stability on initial data in the L2 norm.

scholarly journals ON CONSTRUCTION AND ANALYSIS OF FINITE DIFFERENCE SCHEMES FOR PSEUDOPARABOLIC PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS

2014 ◽  
Vol 19 (2) ◽  
pp. 281-297 ◽  
Author(s):  
Raimondas Čiegis ◽  
Natalija Tumanova
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Two Dimensional ◽  
The Stability

In this paper the one- and two-dimensional pseudoparabolic equations with nonlocal boundary conditions are approximated by the Euler finite difference scheme. In the case of classical boundary conditions the stability of all schemes is investigated by the spectral method. Stability regions of finite difference schemes approximating pseudoparabolic problem are compared with the stability regions of the classical discrete parabolic problem. These results are generalized for problems with nonlocal boundary conditions if a matrix of the finite difference scheme can be diagonalized. For the two-dimensional problem an efficient algorithm is constructed, which is based on the combination of the FFT method and the factorization algorithm. General stability results, known for the three level finite difference schemes, are applied to investigate the stability of some explicit approximations of the two-dimensional pseudoparabolic problem with classical boundary conditions. A connection between the energy method stability conditions and the spectrum Hurwitz stability criterion is shown. The obtained results can be applied for pseudoparabolic problems with nonlocal boundary conditions, if a matrix of the finite difference scheme can be diagonalized.

Pemanfaatan Metil Ester Sulfonat pada Pembuatan Deterjen Cair

2016 ◽  
Vol 7 (14) ◽  
pp. 143-155
Author(s):  
Eldha Sampepana ◽  
Suroto Hadi Saputra
Keyword(s):  
Fatty Acids ◽  
Methyl Ester ◽  
Linear Alkylbenzene Sulfonate ◽  
Emulsion Stability ◽  
Alcohol Sulfate ◽  
Stable Emulsion ◽  
Linear Alkylbenzene ◽  
Alkylbenzene Sulfonate ◽  
The Stability ◽  
The Right

In the manufacture of detergents still using surfactants (which serves as an emulsifier) of crude oil in the form of the AS. (alcohol sulfate) and LAS (linear alkylbenzene sulfonate), where this type of surfactant cannot be degraded by microorganisms when discharged into the environment, causing environmental pollution. Methyl ester sulfonate surfactant is an anionic surfactant which has a composition of C16 - C18 fatty acids are capable of acting against nature deterjensinya, while the C12 - C14 fatty acids contribute to the foaming effect. The purpose of this study was to look for the formulation of methyl ester sulfonate (MES) the right to produce a good detergent by using materials such as methyl ester sulfonate surfactant self-made, methyl ester sulfonate and sodium lauryl market Ester Sulfate (SLS) with a concentration of 15 %, 20 % and 25 %. Detergent results of the study have high detergency ( net ) compared with the detergency of detergent commercial, have a stable emulsion stability, the stability of the foam/foam detergent power made from methyl ester sulfonate surfactant produces less foam, compared with a detergent made from SLS and surfactant SNI 06-4075-1996 standards.

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

scholarly journals High-Speed Video Analysis of the Process Stability in Plasma Spraying

2021 ◽  
Author(s):  
K. Bobzin ◽  
M. Öte ◽  
M. A. Knoch ◽  
I. Alkhasli ◽  
H. Heinemann
Keyword(s):  
Plasma Spraying ◽  
High Speed ◽  
Plasma Jet ◽  
Plasma Jets ◽  
Time Dependent ◽  
Acquisition Time ◽  
Fast Fourier Transformation ◽  
Frequency Spectra ◽  
Dependent Signal ◽  
The Stability

AbstractIn plasma spraying, instabilities and fluctuations of the plasma jet have a significant influence on the particle in-flight temperatures and velocities, thus affecting the coating properties. This work introduces a new method to analyze the stability of plasma jets using high-speed videography. An approach is presented, which digitally examines the images to determine the size of the plasma jet core. By correlating this jet size with the acquisition time, a time-dependent signal of the plasma jet size is generated. In order to evaluate the stability of the plasma jet, this signal is analyzed by calculating its coefficient of variation cv. The method is validated by measuring the known difference in stability between a single-cathode and a cascaded multi-cathode plasma generator. For this purpose, a design of experiment, covering a variety of parameters, is conducted. To identify the cause of the plasma jet fluctuations, the frequency spectra are obtained and subsequently interpreted by means of the fast Fourier transformation. To quantify the significance of the fluctuations on the particle in-flight properties, a new single numerical parameter is introduced. This parameter is based on the fraction of the time-dependent signal of the plasma jet in the relevant frequency range.

scholarly journals Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity

2021 ◽  
Vol 11 (11) ◽  
pp. 4833
Author(s):  
Afroja Akter ◽  
Md. Jahedul Islam ◽  
Javid Atai
Keyword(s):  
Numerical Stability ◽  
Bragg Gratings ◽  
Stability Boundaries ◽  
Quintic Nonlinearity ◽  
Numerical Stability Analysis ◽  
Gap Solitons ◽  
The Stability ◽  
Dual Core

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

Tertiary solutions and their stability in rotating plane Couette flow

1998 ◽  
Vol 358 ◽  
pp. 357-378 ◽  
Author(s):  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Stability Boundary ◽  
Streamwise Vortex ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Plane Couette Flow ◽  
Streamwise Direction ◽  
The Stability ◽  
Oscillatory Instabilities

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).

Sign in / Sign up

Export Citation Format

Share Document