In applied mathematics Strang splitting is a numerical method for solving differential equations that are decomposable into a sum of differential operators.
It is used to speed up calculation for problems involving operators on very different time scales, for example, chemical reactions in fluid dynamics, and to solve multidimensional partial differential equations by reducing them to a sum of one-dimensional problems.
As a precursor to Strang splitting, consider a differential equation of the form where
were constant coefficient matrices, then the exact solution to the associated initial value problem would be If
commute, then by the exponential laws this is equivalent to If they do not, then by the Baker–Campbell–Hausdorff formula it is still possible to replace the exponential of the sum by a product of exponentials at the cost of a second order error: This gives rise to a numerical scheme where one, instead of solving the original initial problem, solves both subproblems alternating: In this context,
is a numerical scheme solving the subproblem to first order.
Instead of taking full time steps with each operator, instead, one performs time steps as follows: One can prove that Strang splitting is second order by using either the Baker-Campbell-Hausdorff formula, Rooted tree analysis or a direct comparison of the error terms using Taylor expansion.