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Trigonometric integrators for quasilinear wave equations

Publication ,  Journal Article
Gauckler, L; Lu, J; Marzuola, JL; Rousset, F; Schratz, K
Published in: Mathematics of Computation
January 1, 2019

Trigonometric time integrators are introduced as a class of explicit numerical methods for quasilinear wave equations. Second-order convergence for the semidiscretization in time with these integrators is shown for a sufficiently regular exact solution. The time integrators are also combined with a Fourier spectral method into a fully discrete scheme, for which error bounds are provided without requiring any CFL-type coupling of the discretization parameters. The proofs of the error bounds are based on energy techniques and on the semiclassical Gårding inequality.

Duke Scholars

Published In

Mathematics of Computation

DOI

ISSN

0025-5718

Publication Date

January 1, 2019

Volume

88

Issue

316

Start / End Page

717 / 749

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Gauckler, L., Lu, J., Marzuola, J. L., Rousset, F., & Schratz, K. (2019). Trigonometric integrators for quasilinear wave equations. Mathematics of Computation, 88(316), 717–749. https://doi.org/10.1090/mcom/3339
Gauckler, L., J. Lu, J. L. Marzuola, F. Rousset, and K. Schratz. “Trigonometric integrators for quasilinear wave equations.” Mathematics of Computation 88, no. 316 (January 1, 2019): 717–49. https://doi.org/10.1090/mcom/3339.
Gauckler L, Lu J, Marzuola JL, Rousset F, Schratz K. Trigonometric integrators for quasilinear wave equations. Mathematics of Computation. 2019 Jan 1;88(316):717–49.
Gauckler, L., et al. “Trigonometric integrators for quasilinear wave equations.” Mathematics of Computation, vol. 88, no. 316, Jan. 2019, pp. 717–49. Scopus, doi:10.1090/mcom/3339.
Gauckler L, Lu J, Marzuola JL, Rousset F, Schratz K. Trigonometric integrators for quasilinear wave equations. Mathematics of Computation. 2019 Jan 1;88(316):717–749.
Journal cover image

Published In

Mathematics of Computation

DOI

ISSN

0025-5718

Publication Date

January 1, 2019

Volume

88

Issue

316

Start / End Page

717 / 749

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics