Splitting and composition methods with embedded error estimators
For researchers using numerical integration methods, this work provides a practical way to estimate errors and adapt step sizes with low overhead.
The paper introduces new local error estimators for splitting and composition methods that require minimal additional computation, enabling adaptive step size control. Numerical examples demonstrate the efficiency of the approach.
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the additional computational cost required for their evaluation is almost insignificant. These estimators can be subsequently used to adapt the step size along the integration. Numerical examples show the efficiency of the procedure.