# Non-existence of generalized splitting methods with positive coefficients of order higher than four

## TL;DR

This paper proves that generalized exponential splitting methods with positive coefficients cannot achieve an order higher than four, extending the known limitation from classical methods of order two.

## Contribution

It establishes a fundamental limitation on the order of generalized exponential splitting methods with positive real coefficients, generalizing previous results.

## Key findings

- Limit of order four for generalized exponential splitting methods with positive coefficients
- Extension of classical order two restriction to higher-order methods
- Theoretical proof of non-existence for higher-order methods with positive coefficients

## Abstract

We prove that generalized exponential splitting methods making explicit use of commutators of the vector fields are limited to order four when only real coefficients are admitted. This generalizes the restriction to order two for classical splitting methods with only positive coefficients.