# Splitting and composition methods with embedded error estimators

## TL;DR

This paper introduces new local error estimators for splitting and composition methods that enable efficient adaptive step sizing with minimal additional computational cost, demonstrated through numerical examples.

## Contribution

The authors develop novel local error estimators based on linear combinations of intermediate stages, enhancing adaptive step size control in splitting and composition methods.

## Key findings

- Estimators are computationally inexpensive to evaluate.
- Adaptive step sizing improves integration efficiency.
- Numerical tests confirm estimator effectiveness.

## Abstract

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.