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Difference Methods for Stochastic Partial Differential Equations
Author(s) -
Roth Ch.
Publication year - 2002
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200211)82:11/12<821::aid-zamm821>3.0.co;2-l
Subject(s) - stochastic partial differential equation , mathematics , hyperbolic partial differential equation , numerical partial differential equations , partial differential equation , stochastic differential equation , first order partial differential equation , consistency (knowledge bases) , convergence (economics) , mathematical analysis , discrete mathematics , economics , economic growth
The present article focuses on the use of difference methods in order to approximate the solutions of stochastic partial differential equations of Itô‐type, in particular hyperbolic equations. The main notions of deterministic difference methods, i.e. convergence, consistency, and stability, are developped for the stochastic case. It is shown that the proposed stochastic difference schemes for several partial differential equations have these properties.