Abstract. We show that the abstract operator-theoretic (general) Trotter--Kato formulae yield the convergence of numerical methods used for solving differential equations. These methods combine operator splitting procedures with certain time discretisation schemes which should be consistent, strongly A-stable, positive rational approximations of the exponential function. We also show that it is possible to apply more numerical steps in one splitting time step and the convergence results remain true.

DOI: 10.14232/actasm-020-140-3

AMS Subject Classification (1991): 47D06, 65M12

Keyword(s): operator semigroups, operator splittings, time discretisation schemes, Trotter--Kato product formula, numerical solution of differential equations

received 9.11.2020, revised 13.1.2021, accepted 2.2.2021. (Registered under 140/2020.)