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
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
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
Order Conditions of Stochastic Runge--Kutta Methods by B-Series
SIAM Journal on Numerical Analysis
Numerical Integration of Stochastic Differential Equations with Nonglobally Lipschitz Coefficients
SIAM Journal on Numerical Analysis
Continuous weak approximation for stochastic differential equations
Journal of Computational and Applied Mathematics
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In the present paper, a class of stochastic Runge-Kutta methods containing the second order stochastic Runge-Kutta scheme due to E. Platen for the weak approximation of Ito stochastic differential equation systems with a multi-dimensional Wiener process is considered. Order 1 and order 2 conditions for the coefficients of explicit stochastic Runge-Kutta methods are solved and the solution space of the possible coefficients is analyzed. A full classification of the coefficients for such stochastic Runge-Kutta schemes of order 1 and two with minimal stage numbers is calculated. Further, within the considered class of stochastic Runge-Kutta schemes coefficients for optimal schemes in the sense that additionally some higher order conditions are fulfilled are presented.