Geodesic
Analysis of a splitting scheme for a class of random nonlinear partial differential equations
Duboscq, Romain1  ; Marty, Renaud2 
1 Institut Mathématique de Toulouse, 118 route de Narbonne, 31062 Toulouse, cedex, France.
2 Universitéde Lorraine, CNRS, Institut Elie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy, 54506, France.
ESAIM: Probability and Statistics, Tome 20 (2016), pp. 572-589

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In this paper, we consider a Lie splitting scheme for a nonlinear partial differential equation driven by a random time-dependent dispersion coefficient. Our main result is a uniform estimate of the error of the scheme when the time step goes to 0. Moreover, we prove that the scheme satisfies an asymptotic-preserving property. As an application, we study the order of convergence of the scheme when the dispersion coefficient approximates a (multi)fractional process.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2016023
Classification : 35Q55, 65M15, 60H15, 60F17
Keywords: Nonlinear partial differential equations, splitting, stochastic partial differential equations, asymptotic-Preserving schemes, fractional and multifractional processes

Duboscq, Romain 1 ; Marty, Renaud 2

1 Institut Mathématique de Toulouse, 118 route de Narbonne, 31062 Toulouse, cedex, France.
2 Universitéde Lorraine, CNRS, Institut Elie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy, 54506, France. 
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     author = {Duboscq, Romain and Marty, Renaud},
     title = {Analysis of a splitting scheme for a class of random nonlinear partial differential equations},
     journal = {ESAIM: Probability and Statistics},
     pages = {572--589},
     publisher = {EDP-Sciences},
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     year = {2016},
     doi = {10.1051/ps/2016023},
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     zbl = {1358.35168},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2016023/}
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Duboscq, Romain; Marty, Renaud. Analysis of a splitting scheme for a class of random nonlinear partial differential equations. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 572-589. doi: 10.1051/ps/2016023

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