TY - JOUR

T1 - Numerical analysis of semilinear stochastic evolution equations in Banach spaces

AU - Hausenblas, Erika

PY - 2002

Y1 - 2002

N2 - The solution of stochastic evolution equations generally relies on numerical computation. Here, usually the main idea is to discretize the SPDE spatially obtaining a system of SDEs that can be solved by e.g., the Euler scheme. In this paper, we investigate the discretization error of semilinear stochastic evolution equations in Lp-spaces, resp. Banach spaces. The space discretization may be done by Galerkin approximation, for the time discretization we consider the implicit Euler, the explicit Euler scheme and the Crank-Nicholson scheme. In the last section, we give some examples i.e., we consider an SPDEs driven by nuclear Wiener noise approximated by wavelets and delay equation approximated by finite differences.

AB - The solution of stochastic evolution equations generally relies on numerical computation. Here, usually the main idea is to discretize the SPDE spatially obtaining a system of SDEs that can be solved by e.g., the Euler scheme. In this paper, we investigate the discretization error of semilinear stochastic evolution equations in Lp-spaces, resp. Banach spaces. The space discretization may be done by Galerkin approximation, for the time discretization we consider the implicit Euler, the explicit Euler scheme and the Crank-Nicholson scheme. In the last section, we give some examples i.e., we consider an SPDEs driven by nuclear Wiener noise approximated by wavelets and delay equation approximated by finite differences.

UR - http://dx.doi.org/10.1016/S0377-0427(02)00483-1

U2 - 10.1016/S0377-0427(02)00483-1

DO - 10.1016/S0377-0427(02)00483-1

M3 - Article

VL - 147.2002

SP - 485

EP - 516

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 1879-1778

IS - 2

ER -