In this paper we discuss the extension to exponential splitting methods with respect to time-dependent operators. We concentrate on the Suzuki’s method, which incorporates ideas to the time-ordered exponential of [3,11,12,34]. We formulate the methods with respect to higher order by using kernels for an extrapolation scheme. The advantages include more accurate and less computational intensive schemes to special time-dependent harmonic oscillator problems. The benefits of the higher order kernels are given on different numerical examples.
