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Error analysis of splitting methods for semilinear evolution equations

Masahito Ohta, Takiko Sasaki (2017)

Applications of Mathematics

We consider a Strang-type splitting method for an abstract semilinear evolution equation t u = A u + F ( u ) . Roughly speaking, the splitting method is a time-discretization approximation based on the decomposition of the operators A and F . Particularly, the Strang method is a popular splitting method and is known to be convergent at a second order rate for some particular ODEs and PDEs. Moreover, such estimates usually address the case of splitting the operator into two parts. In this paper, we consider the splitting...

Error estimates for external approximation of ordinary differential equations and the superconvergence property

Teresa Regińska (1988)

Aplikace matematiky

A pointwise error estimate and an estimate in norm are obtained for a class of external methods approximating boundary value problems. Dependence of a superconvergence phenomenon on the external approximation method is studied. In this general framework, superconvergence at the knot points for piecewise polynomial external methods is established.

Erweiterung des G -Stabilitätsbegriffes auf die Klasse der linearen Mehrschrittblockverfahren.

Reiner Vanselow (1983)

Aplikace matematiky

In der vorliegenden Arbeit wird der G -Stabilitätsbegriff von Dahlquist, der die Grundlage für Stabilitätsuntersuchungen bei linearen Mehrschrittverfahren zur Lösung nichtlinearet Anfangswertaufgaben bildet, auf die Klasse der linearen Mehrschrittblockverfahren übertragen. Es wird nachgewiesen, das Blockverfahren, die in diesem Sinne stabil sind, höchstens die Konsistenzordnung 2 haben können.

Essential self-adjointness of symmetric linear relations associated to first order systems

Matthias Lesch (2000)

Journées équations aux dérivées partielles

The purpose of this note is to present several criteria for essential self-adjointness. The method is based on ideas due to Shubin. This note is divided into two parts. The first part deals with symmetric first order systems on the line in the most general setting. Such a symmetric first order system of differential equations gives rise naturally to a symmetric linear relation in a Hilbert space. In this case even regularity is nontrivial. We will announce a regularity result and discuss criteria...

Estimate for the Number of Zeros of Abelian Integrals on Elliptic Curves

Mihajlova, Ana (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 34C07, secondary 34C08.We obtain an upper bound for the number of zeros of the Abelian integral.The work was partially supported by contract No 15/09.05.2002 with the Shoumen University “K. Preslavski”, Shoumen, Bulgaria.

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