基于切比雪夫多项式逼近的6级6阶隐式Runge-Kutta方法

Six-stage sixth-order implicit Runge-Kutta method based on Chebyshev polynomial approximation

以切比雪夫偏差点为插值点,利用切比雪夫多项式逼近理论和高斯-洛巴托-切比雪夫求积公式,构造了一个6级6阶的隐式Runge-Kutta方法.理论分析发现,该算法具有良好的稳定性——A_0稳定,较大α值的A(α)稳定,较小D值的刚性稳定和几乎L稳定.数值算例显示了该算法的有效性.

Based on the Chebyshev polynomial approximation theory, using Cheby- shev deviation points and Gauss-Lobatto-Chebyshev quadrature formula, a six- stage sixth-order implicit Runge-Kutta method is presented. It is showed that the new algorithm has good stability properties in theoretical analysis, A0-stable, A（a）-stable with a larger value of a, stiff-stable with a smaller value of D and almost L-stable. The numerical examples illustrate its effectiveness.