Accurate Implicit–Explicit General Linear Methods with Inherent Runge–Kutta Stability
Accurate Implicit–Explicit General Linear Methods with Inherent Runge–Kutta Stability
复制标题
具有固有龙格-库塔稳定性的精确隐式-显式一般线性方法
DOI：
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发表时间：
2017
影响因子：
2.5
通讯作者：
Z. Jackiewicz
中科院分区：
文献类型：
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作者：
M. Braś;G. Izzo;Z. Jackiewicz
研究了具有非刚性和刚性过程的微分系统的隐式-显式（IMEX）广义线性方法（GLM）的内在龙格-库塔稳定性（IRKS）。这样的公式的建设开始与IRKS是A-和L-稳定的隐式GLM，然后我们'删除'隐式在非刚性条款外推未知的阶段衍生物阶段衍生物已经计算的方法。然后我们寻找具有显式部分绝对稳定区域的IMEX格式，假设隐式部分对（0，π/2]$$α∈（0，π/2]中的某个$$alpha是$$A（alpha）$$A（α）稳定的.高度稳定的IMEX GLM的例子是$$1le 4$$1≤p≤4。数值算例表明了这些格式的良好性能。
We investigate implicit–explicit (IMEX) general linear methods (GLMs) with inherent Runge–Kutta stability (IRKS) for differential systems with non-stiff and stiff processes. The construction of such formulas starts with implicit GLMs with IRKS which are A- and L-stable, and then we ‘remove’ implicitness in non-stiff terms by extrapolating unknown stage derivatives by stage derivatives which are already computed by the method. Then we search for IMEX schemes with large regions of absolute stability of the ‘explicit part’ of the method assuming that the ‘implicit part’ of the scheme is $$A(alpha )$$A(α)-stable for some $$alpha in (0,pi /2]$$α∈(0,π/2]. Examples of highly stable IMEX GLMs are provided of order $$1le ple 4$$1≤p≤4. Numerical examples are also given which illustrate good performance of these schemes.