Non-Autonomous Dynamics and Product Formula Approximation of Solution Operator - Zagrebnov, Valentin A. (Discontinuity, Nonlinearity, and Complexity, 2026)
The paper is devoted to non-autonomous dynamics, which is generated by positive self-adjoint operator $A$ and a family of non-negative self-adjoint operators $\{B(t)\}_{t≥ 0}$ defined in a separable Hilbert space. It is shown that solution operator $\{U(t,s)\}_{0 ≤ s ≤ t}$ of the evolution equation can be approximated in the operator norm topology by a product formula that involves $A$ and $B(t)$. We also established the rate of convergence of the product formula to the solution operator. These results are proved using the evolution semigroup approach to non-autonomous dynamics.