All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 5 Next

Displaying 81 – 100 of 508

Showing per page

Applications of approximate gradient schemes for nonlinear parabolic equations

Robert Eymard, Angela Handlovičová, Raphaèle Herbin, Karol Mikula, Olga Stašová (2015)

Applications of Mathematics

We develop gradient schemes for the approximation of the Perona-Malik equations and nonlinear tensor-diffusion equations. We prove the convergence of these methods to the weak solutions of the corresponding nonlinear PDEs. A particular gradient scheme on rectangular meshes is then studied numerically with respect to experimental order of convergence which shows its second order accuracy. We present also numerical experiments related to image filtering by time-delayed Perona-Malik and tensor diffusion...

Approximation of control problems involving ordinary and impulsive controls

Fabio Camilli, Maurizio Falcone (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study an approximation scheme for a class of control problems involving an ordinary control v, an impulsive control u and its derivative u ˙ . Adopting a space-time reparametrization of the problem which adds one variable to the state space we overcome some difficulties connected to the presence of u ˙ . We construct an approximation scheme for that augmented system, prove that it converges to the value function of the augmented problem and establish an error estimates in L∞ for this approximation....

Approximation of viscosity solution by morphological filters

Denis Pasquignon (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider in ℝ 2 all curvature equation ∂ u ∂ t = | D u | G ( curv ( u ) ) where G is a nondecreasing function and curv(u) is the curvature of the level line passing by x. These equations are invariant with respect to any contrast change u → g(u), with g nondecreasing. Consider the contrast invariant operator T t : u o → u ( t ) . A Matheron theorem asserts that all contrast invariant operator T can be put in a form ( T u ) ( 𝐱 ) = inf B ∈ ℬ sup 𝐲 ∈ B u ( 𝐱 + 𝐲 ) . We show the asymptotic equivalence of both formulations. More precisely, we show that all curvature equations can be obtained...

Approximation theorem for evolution operators

Rinka Azuma (2003)

Studia Mathematica

This paper is devoted to the study of the approximation problem for the abstract hyperbolic differential equation u'(t) = A(t)u(t) for t ∈ [0,T], where A(t):t ∈ [0,T] is a family of closed linear operators, without assuming the density of their domains.

Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations

Christophe Gomez, Olivier Pinaud (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This work is concerned with the asymptotic analysis of a time-splitting scheme for the Schrödinger equation with a random potential having weak amplitude, fast oscillations in time and space, and long-range correlations. Such a problem arises for instance in the simulation of waves propagating in random media in the paraxial approximation. The high-frequency limit of the Schrödinger equation leads to different regimes depending on the distance of propagation, the oscillation pattern of the initial...

Bérenger/Maxwell with Discontinous Absorptions : Existence, Perfection, and No Loss

Laurence Halpern, Jeffrey Rauch (2012/2013)

Séminaire Laurent Schwartz — EDP et applications

We analyse Bérenger’s split algorithm applied to the system version of the two dimensional wave equation with absorptions equal to Heaviside functions of x j , j = 1 , 2 . The methods form the core of the analysis [11] for three dimensional Maxwell equations with absorptions not necessarily piecewise constant. The split problem is well posed, has no loss of derivatives (for divergence free data in the case of Maxwell), and is perfectly matched.

Central WENO schemes for hyperbolic systems of conservation laws

Doron Levy, Gabriella Puppo, Giovanni Russo (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a family of high-order, essentially non-oscillatory, central schemes for approximating solutions of hyperbolic systems of conservation laws. These schemes are based on a new centered version of the Weighed Essentially Non-Oscillatory (WENO) reconstruction of point-values from cell-averages, which is then followed by an accurate approximation of the fluxes via a natural continuous extension of Runge-Kutta solvers. We explicitly construct the third and fourth-order scheme and demonstrate...

Combined finite element -- finite volume method (convergence analysis)

Mária Lukáčová-Medviďová (1997)

Commentationes Mathematicae Universitatis Carolinae

We present an efficient numerical method for solving viscous compressible fluid flows. The basic idea is to combine finite volume and finite element methods in an appropriate way. Thus nonlinear convective terms are discretized by the finite volume method over a finite volume mesh dual to a triangular grid. Diffusion terms are discretized by the conforming piecewise linear finite element method. In the paper we study theoretical properties of this scheme for the scalar nonlinear convection-diffusion...

Comparison of explicit and implicit difference methods for quasilinear functional differential equations

W. Czernous, Z. Kamont (2011)

Applicationes Mathematicae

We give a theorem on error estimates of approximate solutions for explicit and implicit difference functional equations with unknown functions of several variables. We apply this general result to investigate the stability of difference methods for quasilinear functional differential equations with initial boundary condition of Dirichlet type. We consider first order partial functional differential equations and parabolic functional differential problems. We compare the properties of explicit...

Comparison of explicit and implicit difference schemes for parabolic functional differential equations

Zdzisław Kamont, Karolina Kropielnicka (2012)

Annales Polonici Mathematici

Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that the assumptions on the regularity of the given functions are the same for both methods. It...

Currently displaying 81 – 100 of 508