Exponential Decay for Nonlinear von Kármán Equations with Memory

Exponential decay for Maxwell equations with a boundary memory condition

We study the asymptotic behavior of the solution of the Maxwell equations with the following boundary condition of memory type Eτ (t) = η0H(t)× n + ∫ ∞ 0 η(s)H(t− s)× n ds. We consider a ‘Graffi’ type free energy and we prove that, if the kernel η satisfies the condition η′′ + κ η′ > 0 and the domain Ω is strongly star shaped, then the energy of the solution exponentially decays. We also prove ...

A MODIFIED STEFFENSEN'S METHOD WITH MEMORY FOR NONLINEAR EQUATIONS

In this note, we propose a modification of Steffensen's method with some free parameters. These parameters are then be used for further acceleration via the concept of with memorization. In this way, we derive a fast Steffensen-type method with memory for solving nonlinear equations. Numerical results are also given to support the underlying theory of the article.  

Exponential Decay of Energy for Some Nonlinear Hyperbolic Equations with Strong Dissipation

Yaojun Ye Department of Mathematics and Information Science, Zhejiang University of Science and Technology, Hangzhou 310023, China Correspondence should be addressed to Yaojun Ye, [email protected] Received 14 December 2009; Revised 21 May 2010; Accepted 4 August 2010 Academic Editor: Tocka Diagana Copyright q 2010 Yaojun Ye. This is an open access article distributed under the Creative...

Exponential Decay in Nonlinear Networks1

Adaptive Steffensen-like Methods with Memory for Solving Nonlinear Equations with the Highest Possible Efficiency Indices

The primary goal of this work is to introduce two adaptive Steffensen-like methods with memory of the highest efficiency indices. In the existing methods, to improve the convergence order applied to memory concept, the focus has only been on the current and previous iteration. However, it is possible to improve the accelerators. Therefore, we achieve superior convergence orders and obtain as hi...