Abstract: We proposed a lattice Runge-Kutta-Boltzmann algorithm for solving the Rossler equations. First,  the classical Runge-Kutta formula was used to construct the lattice Boltzmann model, and we obtained higherorder  truncation error. By using the ChapmanEnskog expansion and multiscale expansion technique, we obtained a series of partial differential equations in different time scales and modified Rssler equations. The numerical results show that the obtained model  can be used to solve  the Rossler equations.

Key words: lattice Boltzmann model, Runge-Kutta formula, Rossler equation