scholarly journals ANALYSIS OF STABILITY OF ONE CLASS OF NUMERICAL METHODS OF SECOND ORDER

2019 ◽  
pp. 92-95
Author(s):  
Vasyl Mykhaylovych Zaiats
Keyword(s):  
Numerical Methods ◽  
Second Order ◽  
Stability Conditions ◽  
Difference Formula ◽  
Conservative Systems ◽  
Trapezoid Method ◽  
The Difference ◽  
Analysis Of Stability ◽  
The Stability ◽  
Combined Numerical Methods

The paper deals with the analysis of the stability of a class of second order combined numerical methods based on the trapezoid method and the difference formula, what obtained by the author. The stability conditions for this class of methods are obtained by the example of conservative systems.

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 Novel Second-Order Accurate Implicit Numerical Methods for the Riesz Space Distributed-Order Advection-Dispersion Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
X. Wang ◽  
F. Liu ◽  
X. Chen
Keyword(s):  
Numerical Methods ◽  
Quadrature Rule ◽  
Second Order ◽  
Riesz Space ◽  
Stability And Convergence ◽  
Dispersion Equations ◽  
Advection Dispersion ◽  
Alternating Direction ◽  
The Stability ◽  
Distributed Order

We derive and analyze second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations (RSDO-ADE) in one-dimensional (1D) and two-dimensional (2D) cases, respectively. Firstly, we discretize the Riesz space distributed-order advection-dispersion equations into multiterm Riesz space fractional advection-dispersion equations (MT-RSDO-ADE) by using the midpoint quadrature rule. Secondly, we propose a second-order accurate implicit numerical method for the MT-RSDO-ADE. Thirdly, stability and convergence are discussed. We investigate the numerical solution and analysis of the RSDO-ADE in 1D case. Then we discuss the RSDO-ADE in 2D case. For 2D case, we propose a new second-order accurate implicit alternating direction method, and the stability and convergence of this method are proved. Finally, numerical results are presented to support our theoretical analysis.

On the Stability of Some Linear Nonautonomous Random Systems

1968 ◽  
Vol 35 (1) ◽  
pp. 7-12 ◽  
Author(s):  
E. F. Infante
Keyword(s):  
Random Systems ◽  
Second Order ◽  
Stability Conditions ◽  
Almost Sure Stability ◽  
Stability Properties ◽  
The Stability ◽  
Second Order Equations

A theorem and two corollaries for the almost sure stability of linear nonautonomous random systems are presented. These results are applied to the study of the stability properties of some often encountered second-order equations and the obtained stability conditions are compared to previously known criteria.

The Definition of a Critical Deflection of Compressed Rods with the Creep by the Method of Bubnov-Galerkin

2018 ◽  
Vol 931 ◽  
pp. 127-132
Author(s):  
Batyr M. Yazyev ◽  
Serdar B. Yazyev ◽  
Anatoly P. Grinev ◽  
Elena A. Britikova
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Difference Method ◽  
Stability Problem ◽  
The Finite Element Method ◽  
The Difference ◽  
The Stability ◽  
Definition Of ◽  
The Galerkin Method

The comparison of the numerical methods: the finite element method, the Galerkin Method, the difference method is considered for the study of the stability of the rods. The dependence of the solution of the stability problem on the parameters of the discretization of these numerical methods is studied. It is shown that the mathematical models are sufficiently accurate to analyze the stability of the rods of constant and variable sections.

On The Stability Of Finite-Difference Schemes For Parabolic Equations Subject To Integral Conditions With Applications To Thermoelasticity

2008 ◽  
Vol 8 (4) ◽  
pp. 360-373 ◽  
Author(s):  
M SAPAGOVAS ◽  
Z. JESEVICIUTE
Keyword(s):  
Stability Analysis ◽  
Difference Scheme ◽  
Parabolic Equations ◽  
Finite Difference Schemes ◽  
Stability Conditions ◽  
Spectral Structure ◽  
Integral Conditions ◽  
Implicit Difference Scheme ◽  
The Difference ◽  
The Stability

Abstract The stability of implicit difference scheme for parabolic equations subject to integral conditions, which correspond to the quasi-static flexure of a thermoelastic rod is considered. The stability analysis is based on the spectral structure of matrix of the difference scheme. The stability conditions obtained here differ from those presented in the articles of other authors..

Stability and Oscillation Characteristics of Finite-Element, Finite-Difference, and Weighted-Residuals Methods for Transient Two-dimensional Heat Conduction in Solids

1973 ◽  
Vol 95 (2) ◽  
pp. 235-239 ◽  
Author(s):  
R. V. S. Yalamanchili ◽  
S.-C. Chu
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Von Neumann ◽  
Weighted Residuals ◽  
Difference Formula ◽  
The Difference ◽  
The Stability ◽  
The Galerkin Method ◽  
Difference Expression ◽  
Oscillation Characteristics

The finite-element difference expression was derived by use of the variational principle and finite-element synthesis. Several ordinary finite-difference formulae for the La-placian term were considered. A particular finite-difference formula for the Laplacian term was chosen to bring the difference expressions of finite-element, finite-difference, and weighted-residuals (Galerkin) methods into the same format. The stability criteria were established for all three techniques by use of the general stability, von Neumann, and Dusinberre concepts. The oscillation characteristics were derived for all three techniques. The finite-element method is more conservative than the finite-difference method, but not so conservative as the Galerkin method in both stability and oscillation characteristics.

On explicit stability conditions for a linear fractional difference system

2015 ◽  
Vol 18 (3) ◽  
Author(s):  
Jan Čermák ◽  
István Győri ◽  
Ludĕk Nechvátal
Keyword(s):  
Stability Conditions ◽  
Difference System ◽  
Fractional Difference ◽  
The Difference ◽  
The Stability ◽  
Stability Area

AbstractThe paper describes the stability area for the difference system (Δ

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