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Error Analysis of Exponential Integrators for Nonlinear Wave-Type Equations
- Publication Year :
- 2021
- Publisher :
- KIT-Bibliothek, Karlsruhe, 2021.
-
Abstract
- This thesis is concerned with the time integration of certain classes of nonlinear evolution equations in Hilbert spaces by exponential integrators. We aim to prove error bounds which can be established by including only quantities given by a wellposedness result. In the first part, we consider semilinear wave equations and introduce a class of first- and second-order exponential schemes. A standard error analysis is not possible due to the lack of regularity. We have to employ appropriate filter functions as well as the integration by parts and summation by parts formulas in order to obtain optimal error bounds. In the second part, we propose two exponential integrators of first and second order applied to a class of quasilinear wave-type equations. By a detailed investigation of the differentiability of the right-hand side we derive error bounds in different norms. In the framework we can treat quasilinear Maxwell’s equations in full space and on a smooth domain as well as a class of quasilinear wave equations. In both parts, we include numerical examples to confirm our theoretical findings.
- Subjects :
- a priori error estimates
numerical analysis
time integration
semilinear evolution equations
semmilinear wave equations
Kerr nonlinearity
operator semigroups
abstract error analysis
Maxwell equations
quasilinear evolution equations
quasilinear wave-type equations
ddc:510
Mathematics
exponential integrators
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....6e8e4e352dc248a42a0a38b1252e38b1