Concept

Pafnouti Tchebychev

Publications associées (10)

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We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed nu ...

2018

A new explicit stabilized scheme of weak order one for stiff and ergodic stochastic differential equations (SDEs) is introduced. In the absence of noise, the new method coincides with the classical deterministic stabilized scheme (or Chebyshev method) for ...

MATHICSE2017

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

Assyr Abdulle, Gilles Vilmart

MATHICSE2017

Generalized Gauss Inequalities via Semidefinite Programming

Daniel Kuhn

A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to ...

Springer Verlag2016

Explicit methods for stiff stochastic differential equations

Assyr Abdulle

Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...

Springer-Verlag Berlin2012

Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: A fully discrete spacetime analysis

Assyr Abdulle, Gilles Vilmart

Numerical methods for parabolic homogenization problems combining finite element methods (FEMs) in space with Runge-Kutta methods in time are proposed. The space discretization is based on the coupling of macro and micro finite element methods following th ...

2012

Stabilized or Chebyshev explicit methods have been widely used in the past to solve stiff ordinary differential equations. Making use of special properties of Chebyshev-like polynomials, these methods have favorable stability properties compared to standar ...

2010

Fundamental Stokes eigenmodes in the square: which expansion is more accurate, Chebyshev or Reid-Harris ?

Emmanuel Leriche

The well known Reid-Harris expansions, applied to the stream function formulation, and the Projection-Diffusion Chebyshev Stokes solver, in primitive variables, are used to compute the fundamental Stokes eigenmodes of each of the symmetry families characte ...

2005

Fundamental Stokes eigenmodes in the square: which expansion is more accurate, Chebyshev or Reid-Harris?

Emmanuel Leriche

Springer, Springer US2005

Integration preconditioning of pseudospectral operators. I. Basic linear operators

Jan Sickmann Hesthaven

This paper develops a family of preconditioners for pseudospectral approximations of pth-order linear differential operators subject to various types of boundary conditions. The approximations are based on ultraspherical polynomials with special attention ...

Society for Industrial and Applied Mathematics1998

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