A Necessary and Sufficient Condition for Stability of Difference Schemes for Second-Order Intial Value Problems

1963 ◽  
Vol 11 (2) ◽  
pp. 474-501 ◽  
Author(s):  
Mary Louise Buchanan
Keyword(s):  
Second Order ◽  
Difference Schemes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Stability Of Difference Schemes ◽  
Necessary And Sufficient

scholarly journals Consensus of Discrete Time Second-Order Multiagent Systems with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Zhu
Keyword(s):  
Time Delay ◽  
Convergence Rate ◽  
Theoretical Result ◽  
Multiagent Systems ◽  
Discrete Time ◽  
Second Order ◽  
Sufficient Condition ◽  
Consensus Problem ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The consensus problem for discrete time second-order multiagent systems with time delay is studied. Some effective methods are presented to deal with consensus problems in discrete time multiagent systems. A necessary and sufficient condition is established to ensure consensus. The convergence rate for reaching consensus is also estimated. It is shown that arbitrary bounded time delay can safely be tolerated. An example is presented to illustrate the theoretical result.

scholarly journals On Wiener's Criterion for an Elliptic Equation with Nonuniform Degeneration

2007 ◽  
Vol 14 (4) ◽  
pp. 607-626
Author(s):  
Rabil A. Amanov ◽  
Farman I. Mamedov
Keyword(s):  
Elliptic Equation ◽  
Laplace Equation ◽  
Elliptic Equations ◽  
Second Order ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Boundary Points ◽  
Necessary And Sufficient

Abstract For some class of nonuniformly degenerated elliptic equations of second order, a necessary and sufficient condition for boundary points to be regular is found. This condition is an analogue of Wiener's criterion for the Laplace equation.

scholarly journals Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Chenghua Gao
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Sufficient Condition ◽  
First Eigenvalue ◽  
Necessary And Sufficient Condition ◽  
The First Eigenvalue ◽  
Necessary And Sufficient

This paper is concerned with the existence of solutions for the discrete second-order boundary value problemΔ2u(t-1)+λ1u(t)+g(Δu(t))=f(t),t∈{1,2,…,T},u(0)=u(T+1)=0, whereT>1is an integer,f:{1,…,T}→R,g:R→Ris bounded and continuous, andλ1is the first eigenvalue of the eigenvalue problemΔ2u(t-1)+λu(t)=0,t∈T,u(0)=u(T+1)=0.

scholarly journals Linear distribution processes

1998 ◽  
Vol 11 (1) ◽  
pp. 43-58 ◽  
Author(s):  
L. Bel ◽  
G. Oppenheim ◽  
L. Robbiano ◽  
M. C. Viano
Keyword(s):  
Continuous Time ◽  
Second Order ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Linear Distribution ◽  
Stationary Increments ◽  
Distribution Process ◽  
Necessary And Sufficient

In this paper, we propose a generalization of continuous-time processed defined by Xt=∫f(t−s)dWs, to the case of f being a distribution. We give a necessary and sufficient condition for f, such that the obtained process is a second order distribution process. We study the moments and the regularity of these processes. In addition, we investigate a generalization to processes with stationary increments.

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