Two exponential-type integrators for the “good” Boussinesq equation

  • Alexander Ostermann
  • Chunmei SuEmail author


We introduce two exponential-type integrators for the “good” Boussinesq equation. They are of orders one and two, respectively, and they require lower spatial regularity of the solution compared to classical exponential integrators. For the first integrator, we prove first-order convergence in \(H^r\) for solutions in \(H^{r+1}\) with \(r>1/2\). This new integrator even converges (with lower order) in \(H^r\) for solutions in \(H^r\), i.e., without any additional smoothness assumptions. For the second integrator, we prove second-order convergence in \(H^r\) for solutions in \(H^{r+3}\) with \(r>1/2\) and convergence in \(L^2\) for solutions in \(H^3\). Numerical results are reported to illustrate the established error estimates. The experiments clearly demonstrate that the new exponential-type integrators are favorable over classical exponential integrators for initial data with low regularity.

Mathematics Subject Classification

35Q40 35Q55 65M12 65M15 81Q05 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of InnsbruckInnsbruckAustria
  2. 2.Zentrum MathematikTechnische Universität MünchenGarching bei MünchenGermany

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