The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
2N-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
Order Conditions of Stochastic Runge--Kutta Methods by B-Series
SIAM Journal on Numerical Analysis
Numerical study of interacting particles approximation for integro-differential equations
Journal of Computational Physics
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Runge-Kutta methods that require only two memory locations per variable and have strong local order @c=1.5 for non-commutative systems of stochastic differential equations driven by one Wiener process are devised in this paper. A first step in the derivation is to extend existing deterministic methods to the commutative stochastic case, for which higher accuracy is also obtained. Numerical results are presented to validate the approach.