# The Trotter-Kato theorem and approximation of PDEs

@article{Ito1998TheTT, title={The Trotter-Kato theorem and approximation of PDEs}, author={Kazufumi Ito and Franz Kappel}, journal={Math. Comput.}, year={1998}, volume={67}, pages={21-44} }

- Published 1998 in Math. Comput.
DOI:10.1090/S0025-5718-98-00915-6

We present formulations of the Trotter-Kato theorem for approximation of linear C0-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes’ equation as illustrative examples.