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.References
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Additional Information
- François Delarue
- Affiliation: Université Paris 7, UFR de Mathématiques, Case 7012, 2, Place Jussieu, 75251 Paris Cedex 05, France
- Email: delarue@math.jussieu.fr
- Stéphane Menozzi
- Affiliation: Université Paris 7, UFR de Mathématiques, Case 7012, 2, Place Jussieu, 75251 Paris Cedex 05, France
- MR Author ID: 739222
- Email: menozzi@math.jussieu.fr
- Received by editor(s): March 30, 2006
- Received by editor(s) in revised form: October 31, 2006
- Published electronically: July 26, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 77 (2008), 125-158
- MSC (2000): Primary 65C30; Secondary 60H10, 60H35
- DOI: https://doi.org/10.1090/S0025-5718-07-02008-X
- MathSciNet review: 2353946