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Unconditional stability of difference formulas

Tomáš Roubíček (1983)

Aplikace matematiky

The paper concerns the solution of partial differential equations of evolution type by the finite difference method. The author discusses the general assumptions on the original equation as well as its discretization, which guarantee that the difference scheme is unconditionally stable, i.e. stable without any stability condition for the time-step. A new notion of the $A_{n}$ -acceptability of the integration formula is introduced and examples of such formulas are given. The results can be applied to ordinary...

Une étude d'existence sur certains problèmes paraboliques

Hélène Rios (1979)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Une propriete arithmetique de certains operateurs differentiels.

J.-P. Bezivin (1986/1987)

Manuscripta mathematica

Uniform exponential stability of linear almost periodic systems in Banach spaces.

Cheban, D.N. (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Uniform exponential stability of linear periodic systems in a Banach space.

Cheban, D.N. (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Weak almost periodic and optimal mild solutions of fractional evolution equations.

Debbouche, Amar, El-Borai, Mahmoud M. (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Well-posedness of abstract Cauchy problems.

F. Neubrander (1984)

Semigroup forum

Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions.

Ashyralyev, A. (2007)

Mathematical Problems in Engineering

Well-posedness of the difference schemes of the high order of accuracy for elliptic equations.

Ashyralyev, Allaberen, Sobolevskiĭ, Pavel E. (2006)

Discrete Dynamics in Nature and Society

When unit groups of continuous inverse algebras are regular Lie groups

Helge Glöckner, Karl-Hermann Neeb (2012)

Studia Mathematica

It is a basic fact in infinite-dimensional Lie theory that the unit group $A^{\times}$ of a continuous inverse algebra A is a Lie group. We describe criteria ensuring that the Lie group $A^{\times}$ is regular in Milnor’s sense. Notably, $A^{\times}$ is regular if A is Mackey-complete and locally m-convex.