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In this article, a new time two-mesh (TT-M) finite element (FE) method, which is constructed by a new TT-M algorithm and FE method in space, is proposed and analyzed. The numerical theories and algorithm are shown by solving the fractional water wave model including fractional derivative in time. The TT-M FE algorithm mainly covers three steps: firstly, a nonlinear FE system at some time points based...
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