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.
翻译:引入了新型的第二序列,即明确的稳定龙格-库塔-切比舍夫(Ringge-Kutta-Chebyshev)方法,用于消化-扩散-反应方程式。新方法的稳定性特性和明确可用系数优异,优于现有相对较高的Peclet数计划。新办法的构建基于稳定,使用在建造SK-ROCK(Stochectic Incomplicator SK-ROCK)时首先使用的第二类Chebyshev 多元米亚仪。提出了执行新办法的适应性算法。这种算法能够自动选择每个整合步骤的适当步骤大小、阶段数目和阻隔参数。介绍了显示新算法效率的数值实验。