Operator splitting is a popular divide-and-conquer strategy for solving
differential equations. Typically, the right-hand side of the differential
equation is split into a number of parts that can then be integrated
separately. Many methods are known that split the right-hand side into two
parts. This approach is limiting, however, and there are situations when
3-splitting is more natural and ultimately more advantageous. The second-order
Strang operator-splitting method readily generalizes to a right-hand side
splitting into any number of operators. It is arguably the most popular method
for 3-splitting because of its efficiency, ease of implementation, and
intuitive nature. Other 3-splitting methods exist, but they are less
well-known, and evaluations of their performance in practice are scarce. We
demonstrate the effectiveness of some alternative 3-split, second-order methods
to Strang splitting on two problems: the reaction-diffusion Brusselator, which
can be split into three parts that each have closed-form solutions, and the
kinetic Vlasov--Poisson equations that is used in semi-Lagrangian plasma
simulations. We find alternative second-order 3-operator-splitting methods that
realize efficiency gains of 10\%--20\% over traditional Strang splitting