We present formulations of the Trotter-Kato theorem for approximation of linear C 0 {}_0 -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.
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Ito et al. (1998) studied this question.
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