论文标题
完全自适应的显式稳定集成剂，用于对流扩散反应问题
A fully adaptive explicit stabilized integrator for advection-diffusion-reaction problems
论文作者
论文摘要
引入了一种新型的二阶稳定式runge-kutta-chebyshev方法，用于对流扩散反应方程。由于其有利的稳定性和明确可用的系数，因此新方法的表现优于相对较高的PECLET数字的现有方案。新方案的构建是基于使用第二种Chebyshev多项式稳定的，该多项式首先用于构建随机集成商SK-Rock。提出了一种实施新方案的自适应算法。该算法能够在每个集成步骤中自动选择合适的步长大小，阶段数和阻尼参数。提出了说明新算法效率的数值实验。
A novel second order family of explicit stabilized Runge-Kutta-Chebyshev methods for advection-diffusion-reaction equations is introduced. The new methods outperform existing schemes for relatively high Peclet number due to their favorable stability properties and explicitly available coefficients. The construction of the new schemes is based on stabilization using second kind Chebyshev polynomials first used in the construction of the stochastic integrator SK-ROCK. An adaptive algorithm to implement the new scheme is proposed. This algorithm is able to automatically select the suitable step size, number of stages, and damping parameter at each integration step. Numerical experiments that illustrate the efficiency of the new algorithm are presented.
