Operator splitting for non-autonomous evolution equations
Provides theoretical foundations for operator splitting methods in non-autonomous settings, benefiting researchers in numerical analysis and PDEs.
The paper develops general product formulas for non-autonomous evolution equations using evolution semigroup methods and demonstrates convergence rates for Strang-splitting on an imaginary time Schrödinger equation with time-dependent potential.
We provide general product formulas for the solutions of non-autonomous abstract Cauchy problems. The main technical tool is the application of evolution semigroup methods, allowing the direct application of existing results on autonomous problems. The results are then illustrated by the example of a imaginary time Schrödinger equation with time dependent potential. We also obtain convergence rates for the Strang-splitting applied to this problem.