Numerical solution of kinetic SPDEs via stochastic Magnus expansion

In this paper, we show how the Itô-stochastic Magnus expansion can be used to efficiently solve stochastic partial differential equations (SPDE) with two space variables numerically. To end, will first discretize SPDE in only by utilizing finite difference methods and vectorize resulting equation exploiting its sparsity. As a benchmark, apply it case of Langevin constant coefficients, where an explicit solution is available, compare scheme Euler–Maruyama scheme. We see that superior terms both accuracy especially computational time using single GPU verify variable coefficient case. Notably, speed-ups order ranging form 20 200 compared scheme, depending on target spatial resolution.