A class of implicit peer methods for stiff systems
A class of implicit peer methods for stiff systems
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一类刚性系统的隐式对等方法
DOI：
10.1016/j.cam.2016.06.014
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
R. Weiner
中科院分区：
文献类型：
--
作者：
B. Soleimani;R. Weiner
提出了一类s-阶段隐式两步peer方法，利用前一步的函数值和新的函数值求解刚性微分方程.这允许将阶数增加到p= s，并直接确保零稳定性。对s≤ 6的p= s阶具有最优零稳定性的s-阶段方法，给出了相应的s-阶段方法，并讨论了其稳定性。在特殊的条件下，我们证明了这些方法的一个最优零稳定子类是超收敛的阶为p= s+ 1的变步长。数值试验和与ODE 15的比较显示了这类隐式对等方法的高潜力。
We present a class of s-stage implicit two step peer methods for the solution of stiff differential equations using the function values from the previous step in addition to the new function values. This allows to increase the order to p= s and to ensure zero-stability straightforwardly. Corresponding s-stage methods for s≤ 6 of order p= s with optimal zero stability are presented and their stability is discussed. Under special conditions, we prove that an optimally zero-stable subclass of these methods is superconvergent of order p= s+ 1 for variable step sizes. Numerical tests and comparison with ode15s show the high potential of this class of implicit peer methods.