title: Numerical method based on the lattice Boltzmann model for the Fisher equation.
abstract: In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.
authors.affiliation: Department of Mechanics and Engineering Mathematics, College of Mathematics, Jilin University, Changchun 130012, People's Republic of China. yangw@email.jlu.edu.cn
authors.forename: Guangwu
authors.initials: G
authors.lastname: Yan
authors.forename: Jianying
authors.initials: J
authors.lastname: Zhang
authors.forename: Yinfeng
authors.initials: Y
authors.lastname: Dong
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D004058:Diffusion; D006801:Humans; D008956:Models, Chemical; D008957:Models, Genetic; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D011157:Population Dynamics