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The norm convergence of a Magnus expansion method

100%

Bátkai A., Sikolya E.

Open Mathematics

2012

tom 10

nr 1

150-158

We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method is investigated.

Linear dynamics of semigroups generated by differential operators

88%

Alberto Conejero J., Lizama C., Murillo-Arcila M., Peris A.

Open Mathematics

2017

tom 15

nr 1

745-767

During the last years, several notions have been introduced for describing the dynamical behavior of linear operators on infinite-dimensional spaces, such as hypercyclicity, chaos in the sense of Devaney, chaos in the sense of Li-Yorke, subchaos, mixing and weakly mixing properties, and frequent hypercyclicity, among others. These notions have been extended, as far as possible, to the setting of C0-semigroups of linear and continuous operators. We will review some of these notions and we will discuss basic properties of the dynamics of C0-semigroups. We will also study in detail the dynamics of the translation C0-semigroup on weighted spaces of integrable functions and of continuous functions vanishing at infinity. Using the comparison lemma, these results can be transferred to the solution C0-semigroups of some partial differential equations. Additionally, we will also visit the chaos for infinite systems of ordinary differential equations, that can be of interest for representing birth-and-death process or car-following traffic models.

Ograniczanie wyników

2 Open Mathematics

1 Alberto Conejero J.

1 Bátkai A.

1 Lizama C.

1 Murillo-Arcila M.

1 Peris A.

1 Sikolya E.

1 2017

1 2012

Wyniki wyszukiwania

The norm convergence of a Magnus expansion method

Linear dynamics of semigroups generated by differential operators