Stochastic Runge-Kutta Software Package for Stochastic Differential Equations

A Runge-Kutta Method for Index 1 Stochastic Differential-Algebraic Equations with Scalar Noise

The paper deals with the numerical treatment of stochastic differential-algebraic equations of index one with a scalar driving Wiener process. Therefore, a particularly customized stochastic Runge-Kutta method is introduced. Order conditions for convergence with order 1.0 in the mean-square sense are calculated and coefficients for some schemes are presented. The proposed schemes are stiffly ac...

Fast Communication Two-stage Stochastic Runge-kutta Methods for Stochastic Differential Equations with Jump Diffusion

Supplement: Efficient weak second order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations

This paper gives a modification of a class of stochastic Runge-Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

B-Series Analysis of Stochastic Runge-Kutta Methods That Use an Iterative Scheme to Compute Their Internal Stage Values

In recent years, implicit stochastic Runge–Kutta (SRK) methods have been developed both for strong and weak approximations. For these methods, the stage values are only given implicitly. However, in practice these implicit equations are solved by iterative schemes such as simple iteration, modified Newton iteration or full Newton iteration. We employ a unifying approach for the construction of ...

A new higher-order weak approximation scheme for stochastic differential equations and the Runge-Kutta method

The authors report on the construction of a new algorithm for the weak approximation of stochastic differential equations. In this algorithm, an ODE-valued random variable whose average approximates the solution of the given stochastic differential equation is constructed by using the notion of free Lie algebras. It is proved that the classical Runge–Kutta method for ODEs is directly applicable...