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Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients

Pulin Kumar Bhattacharyya, Neela Nataraj (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Estimates for the combined effect of boundary approximation and numerical integration on the approximation of (simple) eigenvalues and eigenvectors of 4th order eigenvalue problems with variable/constant coefficients in convex domains with curved boundary by an isoparametric mixed finite element method, which, in the particular case of bending problems of aniso-/ortho-/isotropic plates with variable/constant thickness, gives a simultaneous approximation to bending moment tensor field Ψ = ( ψ i j ) 1 ≤ i , j ≤ 2 and displacement...

Isoperimetric estimates for the first eigenvalue of the p -Laplace operator and the Cheeger constant

Bernhard Kawohl, V. Fridman (2003)

Commentationes Mathematicae Universitatis Carolinae

First we recall a Faber-Krahn type inequality and an estimate for λ p ( Ω ) in terms of the so-called Cheeger constant. Then we prove that the eigenvalue λ p ( Ω ) converges to the Cheeger constant h ( Ω ) as p → 1 . The associated eigenfunction u p converges to the characteristic function of the Cheeger set, i.e. a subset of Ω which minimizes the ratio | ∂ D | / | D | among all simply connected D ⊂ ⊂ Ω . As a byproduct we prove that for convex Ω the Cheeger set ω is also convex.

Iterated oscillation criteria for delay partial difference equations

Başak Karpuz, Özkan Öcalan (2014)

Mathematica Bohemica

In this paper, by using an iterative scheme, we advance the main oscillation result of Zhang and Liu (1997). We not only extend this important result but also drop a superfluous condition even in the noniterated case. Moreover, we present some illustrative examples for which the previous results cannot deliver answers for the oscillation of solutions but with our new efficient test, we can give affirmative answers for the oscillatory behaviour of solutions. For a visual explanation of the examples,...

Iterations for nonlocal elliptic problems

Ewa Sylwestrzak (2004)

Banach Center Publications

Convergence of an iteration sequence for some class of nonlocal elliptic problems appearing in mathematical physics is studied.

Iterative Einschliessungen von Lösungen nichtlinearer Differentialgleichungen durch Newton-ähnliche Iterationsverfahren

Rudolf L. Voller (1986)

Aplikace matematiky

In der vorliegenden Arbeit untersuchen wir monoton einschliessende Newton-ähnliche Iterationsverfahren zur näherungsweisen Lösung verschiedener Klassen vonnichtlinearen Differentialgleichungen. Die behandelten Methoden sind auch für nichtkonvexe Nichtlinearitäten anwendbar. Ferner konstruieren wir einschliessende Startnäherungen für diese Verfahren, so dass wir die Existenz der Lösungen der gegebenen Differentialgleichungen sichern können. Die Konvergenz der Verfahren wird auch für den Fall bewiesen,...

Iterative methods for parabolic functional differential equations

Milena Matusik (2013)

Applicationes Mathematicae

This paper is concerned with iterative methods for parabolic functional differential equations with initial boundary conditions. Monotone iterative methods are discussed. We prove a theorem on the existence of solutions for a parabolic problem whose right-hand side admits a Jordan type decomposition with respect to the function variable. It is shown that there exist Newton sequences which converge to the solution of the initial problem. Differential equations with deviated variables and differential...

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