The Trotter-Kato theorem and approximation of PDEs

1998/01/01 by Kazufumi Ito, Franz Kappel · 4 citations
Engineering · Computer Science · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering #Numerical methods for differential equations

paper · pdf · doi:10.1090/s0025-5718-98-00915-6

Abstract

We present formulations of the Trotter-Kato theorem for approximation of linear C <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="Subscript 0"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"/> <mml:mn>0</mml:mn> </mml:msub> <mml:annotation encoding="application/x-tex">₀</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -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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