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

Abstract

We introduce two exponential-type integrators for the "good" Bousinessq equation. They are of orders one and two, respectively, and they require lower regularity of the solution compared to the classical exponential integrators. More precisely, we will prove first-order convergence in Hrfor solutions in H^{r+1} with r > 1/2 for the derived first-order scheme. For the second integrator, we prove second-order convergence in Hrfor solutions in H^{r+3} with r > 1/2 and convergence in L2for 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.