Linear-implicit strong schemes for Itô–Galerkin approximations of parabolic stochastic partial differential equations

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 an γ strong linear-implicit Taylor scheme with time-step Δ applied to the N dimensional Itô-Galerkin SDE for a class of parabolic stochastic partial differential equation (SPDE) with a strongly monotone linear operator with eigenvalues λ1≤λ2≤... in its drift term is then estimated by K(λ^−1/2N + 1 + Δ^γ) where the constant K depends on the initial value, bounds on the other coefficients in the SPDE and the length of the time interval under consideration.