标题： 二阶具有单调稳定性多项式的显式Runge-Kutta-Chebyshev方法 显示英文标题

标题： Explicit Runge-Kutta-Chebyshev methods of second order with monotonic stability polynomial

摘要： 提出了一类新的切比雪夫型族的显式稳定化方法，用于求解适度刚性的常微分方程。除了常规的阶和稳定性条件外，我们还对这些方法施加了额外的限制：其稳定性函数必须在其负实轴上尽可能大的区间内单调递增且为正。尽管所提出的这些方法的稳定性区间比经典的切比雪夫型方法的小，但它们的稳定性函数与指数函数更为一致，具有更凸的稳定性区域以及更小的误差常数。这些性质使得单调方法能够与当代的二阶稳定化方法竞争，这从数值实验的结果中可以得到证明。 显示英文摘要

摘要： A new Chebyshev-type family of stabilized explicit methods for solving mildly stiff ODEs is presented. Besides conventional conditions of order and stability we impose an additional restriction on the methods: their stability function must be monotonically increasing and positive along the largest possible interval of negative real axis. Although stability intervals of the proposed methods are smaller than those of classic Chebyshev-type methods, their stability functions are more consistent with the exponent, they have more convex stability regions and smaller error constants. These properties allow the monotonic methods to be competitive with contemporary stabilized second-order methods, as the presented results of numerical experiments demonstrate.