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Currently displaying 1 – 4 of 4

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Approximation of a semilinear elliptic problem in an unbounded domain

Messaoud Kolli; Michelle Schatzman — 2003

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

Let $f$ be an odd function of a class $C^{2}$ such that $f (1) = 0, f^{'} (0) < 0, f^{'} (1) > 0$ and $x \mapsto f (x) / x$ increases on $[0, 1]$ . We approximate the positive solution of $- Δ u + f (u) = 0,$ on $ℝ_{+}^{2}$ with homogeneous Dirichlet boundary conditions by the solution of $- Δ u_{L} + f (u_{L}) = 0,$ on ${] 0, L [}^{2}$ with adequate non-homogeneous Dirichlet conditions. We show that the error $u_{L} - u$ tends to zero exponentially fast, in the uniform norm.

Approximation of a semilinear elliptic problem in an unbounded domain

Messaoud Kolli; Michelle Schatzman — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

Let be an odd function of a class C such that ƒ(1) = 0,ƒ'(0) < 0,ƒ'(1) > 0 and $x \mapsto f (x) / x$ increases on . We approximate the positive solution of Δ = 0, on $_{+}^{2}$ with homogeneous Dirichlet boundary conditions by the solution of $- Δ u_{L} + f (u_{L}) = 0,$ on ]0,[ with adequate non-homogeneous Dirichlet conditions. We show that the error tends to zero exponentially fast, in the uniform norm.

Direct and elementary approach to enumerate topologies on a finite set.

Kolli, Messaoud — 2007

Journal of Integer Sequences [electronic only]

Finite topologies and partitions.

Benoumhani, Moussa; Kolli, Messaoud — 2010

Journal of Integer Sequences [electronic only]

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