Runge–Kutta Lawson schemes for stochastic differential equations

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

“…(see Debrabant et al [8] for details). Due to the construction of the methods, the convergence properties of the underlying methods are retained (Debrabant et al [8]). Specifically, we have the following theorem:…”

“…Theorem 2.1 (Convergence of stochastic Lawson methods [8]) Let Assumption (1) hold, let X be the solution of SDE (1.2), Y n be the result of the stochastic Lawson method (n = 0, . .…”

“…see also Debrabant et al [8]. The matrices A m have to be chosen such that Assumption 1 is satisfied.…”

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

“…) with a Lawson scheme is now just one step of some appropriate one-step method applied to the transformed system (9), giving V n n+1 , followed by a back-transformation Y n+1 = e L n (t n+1 ) V n n+1 (see [6]). In this paper only Lawson schemes based on the implicit trapezoidal and midpoint rules will be discussed.…”

“…Due the construction of the methods, the convergence properties of the underlying methods are retained ( [6]).…”