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**The Trotter-Kato theorem and approximation of PDEs.**
*(English)*
Zbl 0893.47025

Summary: We present formulations of the Trotter-Kato theorem for approximation of linear C\({}_0\)-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.

### MSC:

47D06 | One-parameter semigroups and linear evolution equations |

47H05 | Monotone operators and generalizations |

35G10 | Initial value problems for linear higher-order PDEs |

35K25 | Higher-order parabolic equations |

35L99 | Hyperbolic equations and hyperbolic systems |

65J10 | Numerical solutions to equations with linear operators |

### Keywords:

semigroups of transformations; Trotter-Kato theorems; numerical approximation of linear evolutionary equations; approximation of linear \(C_0\)-semigroups; hyperbolic equation; wave equation; Stokes’ equation
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\textit{K. Ito} and \textit{F. Kappel}, Math. Comput. 67, No. 221, 21--44 (1998; Zbl 0893.47025)

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### References:

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