An interpolated stochastic algorithm for quasi-linear PDEs

Delarue, François; Menozzi, Stéphane

doi:10.1090/S0025-5718-07-02008-X

An interpolated stochastic algorithm for quasi-linear PDEs
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by François Delarue and Stéphane Menozzi PDF

Math. Comp. 77 (2008), 125-158 Request permission

Abstract:

In this paper, we improve the forward-backward algorithm for quasi-linear PDEs introduced in Delarue and Menozzi (2006). The new discretization scheme takes advantage of the standing regularity properties of the true solution through an interpolation procedure. For the convergence analysis, we also exploit the optimality of the square Gaussian quantization used to approximate the conditional expectations involved. The resulting bound for the error is closely related to the Hölder exponent of the second order spatial derivatives of the true solution and turns out to be more satisfactory than the one previously established.

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