https://doi.org/10.1007/s42967-023-00314-5

Spiteri, R.J. (2023) Beyond Strang: A practical assessment of some second-order 3-splitting methods, Commun. Appl. Math. Comput, https://doi.org/10.1007/s42967-023-00314-5

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 are then 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 analysis and evaluation of their performance in practice are scarce. We demonstrate the effectiveness of some alternative 3-splitting, 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 are 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. Our analysis for the practical assessment of the efficiency of operator-splitting methods includes the computational cost of the integrators and can be used in method design.