Linear-implicit strong schemes for Itô-Galkerin approximations of stochastic PDEs

[摘要] Linear-implicit versions of strong Taylor numerical schemes for finite dimensional Itô stochastic differential equations (SDEs) are shown to have the same order as the original scheme. The combined truncation and global discretization error of anγstrong linear-implicit Taylor scheme with time-stepΔapplied to theNdimensional Itô-Galerkin SDE for a class of parabolic stochastic partial differential equation (SPDE) with a strongly monotone linear operator with eigenvaluesλ1≤λ2≤…in its drift term is then estimated byK(λN+1−½+Δγ)where the constantKdepends on the initial value, bounds on the other coefficients in the SPDE and the length of the time interval under consideration.

[学科分类] 应用数学