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A unified lattice Boltzmann model for some nonlinear partial differential equations. (English) Zbl 1139.35333

Summary: A unified and novel lattice Boltzmann model is proposed for solving nonlinear partial differential equation that has the form \(DU_t + \alpha UU_x + \beta U^nU_x - \gamma U_{xx} + \delta U_{xxx} = F(x,t)\). Numerical results agree well with the analytical solutions and results derived by existing literature, which indicates the present model is satisfactory and efficient on solving nonlinear partial differential equations.

MSC:

35G25 Initial value problems for nonlinear higher-order PDEs
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
35A25 Other special methods applied to PDEs
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