Nonlinear mappings in metric discrete limit spaces and their topological properties.
Note on the paper of I. Fenyö: On the solution of non-linear equations in Banach space
Numerical approaches to rate-independent processes and applications in inelasticity
A conceptual numerical strategy for rate-independent processes in the energetic formulation is proposed and its convergence is proved under various rather mild data qualifications. The novelty is that we obtain convergence of subsequences of space-time discretizations even in case where the limit problem does not have a unique solution and we need no additional assumptions on higher regularity of the limit solution. The variety of general perspectives thus obtained is illustrated on several...
Numerical comparisons of two long-wave limit models
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations 16 (2003) 1039–1064; Pego and Quintero, Physica D 132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically...
Numerical comparisons of two long-wave limit models
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations16 (2003) 1039–1064; Pego and Quintero, Physica D132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically...
Numerical Computation of Nonsimple Turning Points and Cusps.
Numerical considerations of a hybrid proximal projection algorithm for solving variational inequalities
In this paper, some ideas for the numerical realization of the hybrid proximal projection algorithm from Solodov and Svaiter [22] are presented. An example is given which shows that this hybrid algorithm does not generate a Fejér-monotone sequence. Further, a strategy is suggested for the computation of inexact solutions of the auxiliary problems with a certain tolerance. For that purpose, ε-subdifferentials of the auxiliary functions and the bundle trust region method from Schramm and Zowe [20]...
Numerical Error Bounds for Fourth Order Boundary Value Problems, Simultaneous Estimation of u(x) and u"(x).
Numerical integration of differential equations in the presence of first integrals: observer method
We introduce a simple and powerful procedure-the observer method-in order to obtain a reliable method of numerical integration over an arbitrary long interval of time for systems of ordinary differential equations having first integrals. This aim is achieved by a modification of the original system such that the level manifold of the first integrals becomes a local attractor. We provide a theoretical justification of this procedure. We report many tests and examples dealing with a large spectrum...
Numerical methods for solving variational inequalities
Numerical solution of a 1-d elastohydrodynamic problem in magnetic storage devices
In this work we present new numerical methods to simulate the mechanics of head-tape magnetic storage devices. The elastohydrodynamic problem is formulated in terms of a coupled system which is governed by a nonlinear compressible Reynolds equation for the air pressure over the head, and a rod model for the tape displacement. A fixed point algorithm between the solutions of the elastic and hydrodynamic problems is proposed. For the nonlinear Reynolds equation, a characteristics method and a...
Numerical treatment of fixed point applied to the nonlinear Fredholm integral equation.
Obere Schranken für Eigenwerte von Eigenwertaufgaben der Form (...2 I Â?...A Â? B) x = 0 . - Upper Bounds for Eigenvalues of Quadratic Eigenvalue Problem.
On a certain algorithm of eigenvalue localization for normal operators
On a certain class of always convergent sequences and the Rayleigh quotient iterations
On a class of iterative procedures for solving nonlinear equations in Banach spaces
On a class of nonlinear eigenvalue problems
On a finite-element collocation method which reproduces the Padé table
On a method of D. Marsal for equations with positive operators
On a new method for enlarging the radius of convergence for Newton's method
We provide new local and semilocal convergence results for Newton's method. We introduce Lipschitz-type hypotheses on the mth-Frechet derivative. This way we manage to enlarge the radius of convergence of Newton's method. Numerical examples are also provided to show that our results guarantee convergence where others do not.