High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Second order weak Runge-Kutta type for Itô equations
Mathematics and Computers in Simulation
Weak Second Order Conditions for Stochastic Runge--Kutta Methods
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
Applied Numerical Mathematics
Physically consistent simulation of mesoscale chemical kinetics: The non-negative FIS-α method
Journal of Computational Physics
Weak second order S-ROCK methods for Stratonovich stochastic differential equations
Journal of Computational and Applied Mathematics
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Recently, a new class of second order Runge-Kutta methods for Ito stochastic differential equations with a multidimensional Wiener process was introduced by Roszler [A. Roszler, Second order Runge-Kutta methods for Ito stochastic differential equations, Preprint No. 2479, TU Darmstadt, 2006]. In contrast to second order methods earlier proposed by other authors, this class has the advantage that the number of function evaluations depends only linearly on the number of Wiener processes and not quadratically. In this paper, we give a full classification of the coefficients of all explicit methods with minimal stage number. Based on this classification, we calculate the coefficients of an extension with minimized error constant of the well-known RK32 method [J.C. Butcher, Numerical Methods for Ordinary Differential Equations, John Wiley & Sons, West Sussex, 2003] to the stochastic case. For three examples, this method is compared numerically with known order two methods and yields very promising results.