On averaged exponential integrators for semilinear wave equations with solutions of low-regularity

Simone Buchholz, Benjamin Dörich () and Marlis Hochbruck ()
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Simone Buchholz: Karlsruhe Institute of Technology
Benjamin Dörich: Karlsruhe Institute of Technology
Marlis Hochbruck: Karlsruhe Institute of Technology

Partial Differential Equations and Applications, 2021, vol. 2, issue 2, 1-27

Abstract: 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.

Keywords: Highly oscillatory problems; Error bounds; Order-reduction; Time-integration; Second-order evolution equations; Filter functions; Summation-by-parts formula; Primary 65J08; 65M12; 65M15; Secondary 35L05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-020-00045-9

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