ANALYSIS OF A SPLITTING SCHEME FOR A CLASS OF RANDOM NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

被引：7

作者：

Duboscq, Romain ^{[1
]}

Marty, Renaud ^{[2
]}

机构：

[1] Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse, France

[2] Univ Lorraine, CNRS, Inst Elie Cartan de Lorraine, UMR 7502, F-54506 Vandoeuvre Les Nancy, France

来源：

ESAIM-PROBABILITY AND STATISTICS | 2016年 / 20卷

关键词：

Nonlinear partial differential equations; splitting; stochastic partial differential equations; asymptotic-Preserving schemes; fractional and multifractional processes; LONG-RANGE CORRELATIONS; SCHRODINGER-EQUATION; RANDOM-MEDIA; KINETIC-EQUATIONS; TIME; LIMIT; CONVERGENCE; FIELDS;

D O I：

10.1051/ps/2016023

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：572 / 589

页数：18

共 34 条

[1]

Agrawal G. P., 2001, NONLINEAR FIBER OPTI, V3rd

[2] Time splitting for wave equations in random media [J].

Bal, G ;

Ryzhik, L .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2004, 38 (06) :961-987

[3]

Bal G., 2004, COMMUN MATH SCI, V2, P515

[4] On time-splitting spectral approximations for the Schrodinger equation in the semiclassical regime [J].

Bao, WZ ;

Jin, S ;

Markowich, PA .

JOURNAL OF COMPUTATIONAL PHYSICS, 2002, 175 (02) :487-524

[5]

Benassi A, 1997, REV MAT IBEROAM, V13, P19

[6] Order estimates in time of splitting methods for the nonlinear Schrodinger equation [J].

Besse, C ;

Bidégaray, B ;

Descombes, E .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 40 (01) :26-40

[7] AN ASYMPTOTIC PRESERVING SCHEME BASED ON A NEW FORMULATION FOR NLS IN THE SEMICLASSICAL LIMIT [J].

Besse, Christophe ;

Carles, Remi ;

Mehats, Florian .

MULTISCALE MODELING & SIMULATION, 2013, 11 (04) :1228-1260

[8]

Billingsley P., 1968, CONVERGE PROBAB MEAS

[9] Invariance principle, multifractional Gaussian processes and long-range dependence [J].

Cohen, Serge ;

Marty, Renaud .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2008, 44 (03) :475-489

[10] NUMERICAL PASSAGE FROM KINETIC TO FLUID EQUATIONS [J].

CORON, F ;

PERTHAME, B .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1991, 28 (01) :26-42

← 1 2 3 4 →