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This paper discusses analytical and numerical issues related to elliptic equations with random coefficients which are generally nonlinear functions of white noise. Singularity issues are avoided by using the Itô-Skorohod calculus to interpret the interactions between the coefficients and the solution. The solution is constructed by means of the Wiener Chaos (Cameron-Martin) expansions. The existence and uniqueness of the solutions are established under rather weak assumptions, the main of which...

Enclosing methods for perturbed boundary value problems in nonlinear difference equations

Schmidt, Jochen W. (1986)

Equadiff 6

Enclosures and semi-analytic discretization of boundary value problems

c. Grossmann (1994)

Banach Center Publications

Energetics and switching of quasi-uniform states in small ferromagnetic particles

François Alouges, Sergio Conti, Antonio DeSimone, Yvo Pokern (2004)

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

We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We...

Energetics and switching of quasi-uniform states in small ferromagnetic particles

François Alouges, Sergio Conti, Antonio DeSimone, Yvo Pokern (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Energy and Momentum Conserving Methods of Arbitrary Order for the Numerical Integration of Equations of Motion. II. Motion of a System of Particles.

R.A. LaBudde, D. Greenspan (1976)

Numerische Mathematik

Energy and Momentum Conserving Methods of Arbitrary Order for the Numerical Integration of Equations of Motion. I. Motion of a Single Particle.

R.A. LaBudde, D. Greenspan (1975/1976)

Numerische Mathematik

Energy Conserving, Arbitrary Order Numerical Solutions of the N-Body Problem.

Andrzej Marciniak (1984)

Numerische Mathematik

Energy-preserving Runge-Kutta methods

Elena Celledoni, Robert I. McLachlan, David I. McLaren, Brynjulf Owren, G. Reinout W. Quispel, William M. Wright (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

We show that while Runge-Kutta methods cannot preserve polynomial invariants in general, they can preserve polynomials that are the energy invariant of canonical Hamiltonian systems.

Enlarging the Domain of Convergence for Multiple Shooting by the Homotopy Method.

P. Lory (1980)

Numerische Mathematik

Entropy solutions to parabolic equations in Musielak framework involving non coercivity term in divergence form

Mohamed Saad Bouh Elemine Vall, Ahmed Ahmed, Abdelfattah Touzani, Abdelmoujib Benkirane (2018)

Mathematica Bohemica

We prove the existence of solutions to nonlinear parabolic problems of the following type: $\{\begin{matrix} \frac{\partial b (u)}{\partial t} + A (u) = f + div (Θ (x; t; u)) & in Q, \\ u (x; t) = 0 & on \partial Ω \times [0; T], \\ b (u) (t = 0) = b (u_{0}) & on Ω, \end{matrix}$ where $b : ℝ \to ℝ$ is a strictly increasing function of class $𝒞^{1}$ , the term $A (u) = - div (a (x, t, u, \nabla u))$ is an operator of Leray-Lions type which satisfies the classical Leray-Lions assumptions of Musielak type, $Θ : Ω \times [0; T] \times ℝ \to ℝ$ is a Carathéodory, noncoercive function which satisfies the following condition: ${sup}_{| s | \leq k} | Θ (\cdot, \cdot, s) | \in E_{ψ} (Q)$ for all $k > 0$ , where $ψ$ is the Musielak complementary function of $Θ$ , and the second term $f$ belongs to $L^{1} (Q)$ .

Epsilon-inflation with contractive interval functions

Günter Mayer (1998)

Applications of Mathematics

For contractive interval functions $[g]$ we show that $[g] ({[x]}_{ϵ}^{k_{0}}) \subseteq \int ({[x]}_{ϵ}^{k_{0}})$ results from the iterative process ${[x]}^{k + 1} : = [g] ({[x]}_{ϵ}^{k})$ after finitely many iterations if one uses the epsilon-inflated vector ${[x]}_{ϵ}^{k}$ as input for $[g]$ instead of the original output vector ${[x]}^{k}$ . Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.

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Einige Stabilitätsungleichungen für gewöhnliche Differenzengleichungen in nichtkompakter Form.

Einschließungsaussagen bei Differentialoperatoren zweiter Ordnung durch punktweise Ungleichungen.

Einschliessungsaussagen für Differentialoperatoren vierter Ordnung und ein Verfahren zur Berechnung von Schrankenfunktionen.

Einschließungsaussagen für gewöhnliche Differentialoperatoren. -Range-Domain Implications for Ordinary Differential Operators.

Elliptic equations of higher stochastic order

Enclosing methods for perturbed boundary value problems in nonlinear difference equations

Enclosures and semi-analytic discretization of boundary value problems

Energetics and switching of quasi-uniform states in small ferromagnetic particles

Energetics and switching of quasi-uniform states in small ferromagnetic particles

Energy and Momentum Conserving Methods of Arbitrary Order for the Numerical Integration of Equations of Motion. II. Motion of a System of Particles.

Energy and Momentum Conserving Methods of Arbitrary Order for the Numerical Integration of Equations of Motion. I. Motion of a Single Particle.

Energy Conserving, Arbitrary Order Numerical Solutions of the N-Body Problem.

Energy-preserving Runge-Kutta methods

Enlarging the Domain of Convergence for Multiple Shooting by the Homotopy Method.

Entropy solutions to parabolic equations in Musielak framework involving non coercivity term in divergence form

Epsilon-inflation with contractive interval functions

Equilibria of Runge-Kutta methods.

Erratum: On the convergence of multistep methods for nonlinear stiff differential equations.

Erratum. On the Reduction of Holt's Problem to a Finite Interval.

Error analysis of Adomian series solution to a class of nonlinear differential equations.

Currently displaying 281 – 300 of 882