In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux+βunux-γuxx+δuxxx= F(U). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective.
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