Runge-Kutta Methods for Rough Differential Equations

We study Runge-Kutta methods for rough differential equations which can be used to calculate solutions stochastic driven by processes that are rougher than a Brownian motion. use Taylor series representation (B-series) both the numerical scheme and solution of equation in order determine conditions guarantee desired local error underlying method. Subsequently, we prove global given rate. In addition, simplify approximation introducing is based on increments driver equation. This simplified method easily implemented computational cheap since it derivative-free. provide full characterization this implementable meaning necessary sufficient algebraic an optimal convergence case driver, e.g., fractional motion with Hurst index $\frac{1}{4} < H \leq \frac{1}{2}$. conclude paper conducting experiments verifying theoretical rate convergence.