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’ equationReferences:
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