一种用于反应扩散方程的格子Runge-Kutta-Boltzmann模型 A Lattice Runge-Kutta-Boltzmann Model for the Reaction Diffusion Equation

本文构建了一个求解反应扩散方程的格子Runge-Kutta-Boltzmann模型。通过使用经典的Runge-Kutta公式，得到了四阶截断误差。通过Chapmann-Enskog展开和多尺度展开技术，获得了不同时间尺度的系列偏微分方程和修正的反应扩散方程。数值结果表明，本文的模型可以用来求解反应扩散方程。 A lattice Runge-Kutta-Boltzmann model for the reaction diffusion equations is constructed in this paper. By using the classical Runge-Kutta formula, we obtain four-order accuracy of truncation error. The Chapman-Enskog expansion and multi-scale technique are employed in order to obtain a series of equations in different time scales and modify partial differential equations of the reaction diffusion equations. Numerical tests show that the scheme can be used to simulate the reaction diffusion equations.