Structure-preserving stochastic conformal exponential integrator for linearly damped stochastic differential equations

Lawson schemes for highly oscillatory stochastic differential equations and conservation of invariants

“…Exponential methods for solving such problems have in particular been applied in the SPDE setting, mostly, but not exclusively for problems with additive noise. Cohen [4] proposed an exponential method for stochastic oscillators, Yang et al [21] suggested one for damped Hamiltonian systems. Recently, Erdoǧan and Lord [9] presented a quite general approach for constructing exponential integrators for (1.2) with multiplicative noise.…”

Conformal structure‐preserving schemes for damped‐driven stochastic nonlinear Schrödinger equation with multiplicative noise

“…For stochastic systems, [20] presents comprehensive researches on stochastic Hamiltonian system and related algorithms. Structure-preserving stochastic conformal exponential integrator has been applied to solve damped stochastic differential equations in [31]. Since 2013, in order to preserve the intrinsic conservation properties of stochastic systems, Hong and his group have devoted to constructing various stochastic structure-preserving schemes [11,12,14,17,19].…”

Strong convergence of a GBM based tamed integrator for SDEs and an adaptive implementation

“…This takes advantage of linear terms not only in the drift but also in the diffusion which is not the case in earlier exponential integrators such as [21,22], see also the short review in [20]. Recent related work on exponential integrators for SDEs includes [23] looking at second-order weak convergence for Runge-Kutta methods, [24] who propose Magnus type exponential integrators for Stratonovich SDEs and [25] that examines families of Runge-Kutta Lawson schemes and their weak and strong convergences. Specifically we examine new explicit tamed based methods for the semilinear SDE…”