Publication Date:
2019-10-16
Description:
We propose an explicit numerical method for the periodic Korteweg–de Vries equation. Our method is based on a Lawson-type exponential integrator for time integration and the Rusanov scheme for Burgers’ nonlinearity. We prove first-order convergence in both space and time under a mild Courant–Friedrichs–Lewy condition $au =O(h)$, where $au$ and $h$ represent the time step and mesh size for solutions in the Sobolev space $H^3((-pi , pi ))$, respectively. Numerical examples illustrating our convergence result are given.
Print ISSN:
0272-4979
Electronic ISSN:
1464-3642
Topics:
Mathematics
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