Semi-discretization of stochastic

partial differential equations on

by a finite-difference method

Author:
Hyek Yoo

Journal:
Math. Comp. **69** (2000), 653-666

MSC (1991):
Primary 35R60, 60H15, 65M06, 65M15

DOI:
https://doi.org/10.1090/S0025-5718-99-01150-3

Published electronically:
April 28, 1999

MathSciNet review:
1654030

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The paper concerns finite-difference scheme for the approximation of partial differential equations in , with additional stochastic noise. By replacing the space derivatives in the original stochastic partial differential equation (SPDE, for short) with difference quotients, we obtain a system of stochastic ordinary differential equations. We study the difference between the solution of the original SPDE and the solution to the corresponding equation obtained by discretizing the space variable. The need to approximate the solution in with functions of compact support requires us to introduce a scale of weighted Sobolev spaces. Employing the weighted -theory of SPDE, a sup-norm error estimate is derived and the rate of convergence is given.

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Additional Information

**Hyek Yoo**

Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455

Email:
yoo@math.umn.edu

DOI:
https://doi.org/10.1090/S0025-5718-99-01150-3

Keywords:
Stochastic partial differential equations,
finite-difference method,
weighted spaces of Bessel potentials,
embedding theorems,
rate of convergence

Received by editor(s):
March 3, 1998

Received by editor(s) in revised form:
July 10, 1998

Published electronically:
April 28, 1999

Article copyright:
© Copyright 2000
American Mathematical Society