Asymptotically efficient Runge-Kutta methods for a class of ITOˆ and Stratonovich equations
SIAM Journal on Applied Mathematics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Random generation of stochastic area integrals
SIAM Journal on Applied Mathematics
High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Weak Second Order Conditions for Stochastic Runge--Kutta Methods
SIAM Journal on Scientific Computing
Order Conditions of Stochastic Runge--Kutta Methods by B-Series
SIAM Journal on Numerical Analysis
Multi-colored rooted tree analysis of the weak order conditions of a stochastic Runge--Kutta family
Applied Numerical Mathematics
Weak order stochastic Runge-Kutta methods for commutative stochastic differential equations
Journal of Computational and Applied Mathematics
SDELab: A package for solving stochastic differential equations in MATLAB
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Second Order Runge-Kutta Methods for Itô Stochastic Differential Equations
SIAM Journal on Numerical Analysis
Strong first order S-ROCK methods for stochastic differential equations
Journal of Computational and Applied Mathematics
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Some new stochastic Runge-Kutta (SRK) methods for the strong approximation of solutions of stochastic differential equations (SDEs) with improved efficiency are introduced. Their convergence is proved by applying multicolored rooted tree analysis. Order conditions for the coefficients of explicit and implicit SRK methods are calculated. As the main novelty, order 1.0 strong SRK methods with significantly reduced computational complexity for Itô as well as for Stratonovich SDEs with a multidimensional driving Wiener process are presented where the number of stages is independent of the dimension of the Wiener process. Further, an order 1.0 strong SRK method customized for Itô SDEs with commutative noise is introduced. Finally, some order 1.5 strong SRK methods for SDEs with scalar, diagonal, and additive noise are proposed. All introduced SRK methods feature significantly reduced computational complexity compared to well-known schemes.