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.