# How to estimate the local error and the global error for Runge-Kutta method

How to estimate the local error and the global error for Runge-Kutta method used for solve a system of differential equations in practice?

I use Richardson extrapolation for select a adaptive step [Solving Ordinary Differential Equations I - Nonstiff Problems 167-168p].

I seen the following formula for estimate a global error for one differential equation: $\delta_{i+1} = \delta_{i}\cdot e^{\int^{t_{i+1}}_{t_i} \mu ds} + r_k$, where $r_k$ local error at step, $\mu$ - maximal eigen value of $\frac{J + J^T}{2}$ ($J$ is jacobian of system). But I didn't find its explanation and application to system of ODE.