A semi-discrete first-order low regularity exponential integrator for the "good" Boussinesq equation without loss of regularity
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In this paper, we propose a semi-discrete first-order low regularity exponential-type integrator (LREI) for the “good" Boussinesq equation. It is shown that the method is convergent linearly in the space H^r for solutions belonging to H^r+p(r) where 0≤ p(r)≤ 1 is non-increasing with respect to r, which means less additional derivatives might be needed when the numerical solution is measured in a more regular space. Particularly, the LREI presents the first-order accuracy in H^r with no assumptions of additional derivatives when r>5/2. This is the first time to propose a low regularity method which achieves the optimal first-order accuracy without loss of regularity for the GB equation. The convergence is confirmed by extensive numerical experiments.
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