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On averaged exponential integrators for semilinear wave equations with solutions of low-regularity
- Source :
- SN Partial Differential Equations and Applications, 2 (2), Art.-Nr.: 23
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- In this paper we introduce a class of second-order exponential schemes for the time integration of semilinear wave equations. They are constructed such that the established error bounds only depend on quantities obtained from a well-posedness result of a classical solution. To compensate missing regularity of the solution the proofs become considerably more involved compared to a standard error analysis. Key tools are appropriate filter functions as well as the integration-by-parts and summation-by-parts formulas. We include numerical examples to illustrate the advantage of the proposed methods.
- Subjects :
- Class (set theory)
Partial differential equation
Numerical analysis
010103 numerical & computational mathematics
Mathematical proof
Wave equation
Exponential integrator
01 natural sciences
Exponential function
010101 applied mathematics
Filter (large eddy simulation)
Applied mathematics
ddc:510
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 26622971 and 26622963
- Volume :
- 2
- Database :
- OpenAIRE
- Journal :
- Partial Differential Equations and Applications
- Accession number :
- edsair.doi.dedup.....1a34618273c238d0a6c7c8391b61d2b1