| Contents |
| In this talk, I propose an exponential explicit integrator for the time discretization of quasilinear parabolic problems. My numerical scheme is based on splitting methods. In an abstract
formulation, the initial-boundary value problem is written as an initial value problem on a Banach space~$X$
\begin{equation}
u'(t) = A\big(u(t)\big) u(t)+ b(t), \quad 0 < t \leq T, \qquad
u(0) \,\,\,{\rm given},
\end{equation}
involving the sectorial operator $A(v):D(v) \to X$ with variable domains $D(v) \subset X$ with regard to $v \in V \subset X$. Under reasonable regularity requirements on the problem, I analyze the stability, the convergence behaviour and some numerical examples
of the numerical methods.
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\bibitem{HochLu} M.~Hochbruck and Ch.~Lubich, \emph{On Magnus integrators for
time-dependent Schr\"odinger equations}. SIAM J.~Numer.~Anal. 41 (2003) pp. 945-963.
\bibitem{HochOs} M.~Hochbruck and A.~Ostermann, \emph{Exponential multistep methods of Adams-type}. BIT, vol. 51, pp. 889-908 (2011).
\bibitem{Thal} M.~Thalhammer, \emph{Convergence analysis of high-order time-splitting pseudospectral methos for nonlinear Schr\"odinger equations}. SIAM J.~Numer.~Anal. 41, vol. 50, No. 6, (2012), pp. 3231-3258.
\end{thebibliography} |
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