Arash Fahim

  1. Strong Convergence to the Homogenized Limit of Parabolic Equations with Random Coefficients.

    Authors: Joseph G. Conlon, Arash Fahim
    Subjects: Analysis of PDEs
    Abstract

    This paper is concerned with the study of solutions to discrete parabolic
    equations in divergence form with random coefficients, and their convergence to
    solutions of a homogenized equation. It has previously been shown that if the
    random environment is translational invariant and ergodic, then solutions of
    the random equation converge under diffusive scaling to solutions of a
    homogenized parabolic PDE.

  2. A Stochastic Approximation for Fully Nonlinear Free Boundary Problems.

    Authors: Erhan Bayraktar, Arash Fahim
    Subjects: Numerical Analysis
    Abstract

    We present a stochastic numerical method for solving fully non-linear free
    boundary problems of parabolic type and provide a rate of convergence under
    reasonable conditions on the non-linearity.

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