Abstract
Focusing on the local conservation properties, a nine-point implicit difference scheme derived from the multi-symplectic idea, which is named as a generalized multi-symplectic integrator, is presented for the Burgers equation firstly. And then, the associated proofs needed on the local conservation properties of the scheme are given in detail. Finally, to illustrate the high accuracy, the good local conservation properties as well as the excellent long-time numerical behavior of the scheme, the numerical experiments on the single-front solution of the Burgers equation by the implicit scheme are reported.
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