Analysis of split exponential integrators for semilinear problems with noncommuting operators

Splitting the exponential and exponential-like functions can significantly reduce the overall computational cost of exponential integrators, providing a strong motivation for their rigorous analysis. In this paper, we analyze splitting errors for two noncommuting unbounded operators and derive new representations that include the popular Lie–Trotter and Strang cases. Moreover, within the abstract framework of strongly continuous semigroups, we prove the convergence of a split version of the exponential Euler method and a second-order exponential Runge–Kutta method for semilinear problems. Numerical experiments on a nonlinear dispersive equation and a diffusion–reaction equation demonstrate the theoretical findings, stability properties, and efficiency of the proposed split exponential integrators compared to the state of the art.