METHOD OF LINES FOR PARABOLIC STOCHASTIC FUNCTIONAL PARTIAL DIFFERENTIAL EQUATIONS

被引：0

作者：

Ziemlanska, Maria ^{[1
]}

机构：

[1] Univ Gdansk, Inst Math, Wit Stwosz St 57, PL-80952 Gdansk, Poland

来源：

OPUSCULA MATHEMATICA | 2014年 / 34卷 / 02期

关键词：

stochastic partial differential equations; stability of the method of lines; white noise; Volterra stochastic equations;

D O I：

10.7494/OpMath.2014.34.2.443

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We approximate parabolic stochastic functional differential equations substituting the derivatives in the space variable by finite differences. We prove the stability of the method of lines corresponding to a parabolic SPDE driven by Brownian motion.

引用

页码：443 / 456

页数：14

共 24 条

[1]

[Anonymous], 1975, STOCHASTIC DIFFERENT

[2]

Bebernes J., 1981, COMP TECHNIQUES METH

[3] Interacting particles, the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, and duality [J].

Doering, CR ;

Mueller, C ;

Smereka, P .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2003, 325 (1-2) :243-259

[4] The method of lines applied to nonlinear nonlocal functional differential equations [J].

Dubey, Shruti A. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 376 (01) :275-281

[5] THE PROPAGATION OF TRAVELING WAVES FOR STOCHASTIC GENERALIZED KPP EQUATIONS [J].

ELWORTHY, KD ;

ZHAO, HZ ;

GAINES, JG .

MATHEMATICAL AND COMPUTER MODELLING, 1994, 20 (4-5) :131-166

[6] The wave of advance of advantageous genes [J].

Fisher, RA .

ANNALS OF EUGENICS, 1937, 7 :355-369

[7] Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise I [J].

Gyongy, I .

POTENTIAL ANALYSIS, 1998, 9 (01) :1-25

[8] Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise [J].

Gyongy, I ;

Nualart, D .

POTENTIAL ANALYSIS, 1997, 7 (04) :725-757

[9]

Hale J., 1993, INTRO FUNCTIONAL DIF

[10] Method of lines solutions of the extended Boussinesq equations [J].

Hamdi, S ;

Enright, WH ;

Ouellet, Y ;

Schiesser, WE .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 183 (02) :327-342

← 1 2 3 →