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arxiv 2104.01249 v2 pith:UA5RKPH2 submitted 2021-04-02 math.FA math.AP

Upper and lower estimates for rate of convergence in the Chernoff product formula for semigroups of operators

Oleg E. Galkin , Ivan D. Remizov This is my paper
classification math.FA math.AP
keywords chernoffapproximationsconvergencearbitrarydifferentialequationsestimatesnorm
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Chernoff approximations to strongly continuous one-parameter semigroups give solutions to a wide class of differential equations. This paper studies the rate of convergence of the Chernoff approximations. We provide simple natural examples for which the convergence is arbitrary fast, is arbitrary slow, and holds in the strong operator topology but does not hold in the norm operator topology. We also prove a general theorem that gives an upper estimate for the speed of decay of the norm of the residual term of the Chernoff approximations. The result is applied to one-dimensional parabolic differential equations with variable coefficients. The obtained estimates can be used for the numerical solution of PDEs.

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  1. Quasi-Feynman formulas that provide fast converging Chernoff approximations to solution of parabolic differential equation on the real line

    math.NA 2026-06 unverdicted novelty 5.0

    Constructs a new class of quasi-Feynman formulas via Chernoff product formula that achieve quadratic uniform convergence for parabolic PDEs with variable coefficients on the real line.