Unconditional Stability for Multistep ImEx Schemes: Theory
Unconditional Stability for Multistep ImEx Schemes: Theory
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DOI：
10.1137/16m1094324
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
R. Rosales;Benjamin Seibold;D. Shirokoff;Dong Zhou
中科院分区：
文献类型：
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作者：
R. Rosales;Benjamin Seibold;D. Shirokoff;Dong Zhou
本文提出了一类新的高阶线性ImEx多步格式，该格式具有大的无条件稳定区域。无条件稳定性是时间步进方案的理想属性，因为它允许仅基于精度考虑来选择时间步长。特别令人感兴趣的是问题的隐式和显式部分的ImEx分裂是僵硬的。例如，在变系数问题或不可压缩Navier-Stokes方程中，可能会出现这种分裂。为了表征新的ImEx格式，引入了一个无条件稳定区域，它起着类似于传统多步法中的稳定区域的作用。此外，可计算的数量（如数值范围），保证一个无条件稳定的计划提出的隐式-显式矩阵分裂。新的方法说明了几个例子。给出了新格式的五阶系数。
This paper presents a new class of high order linear ImEx multistep schemes with large regions of unconditional stability. Unconditional stability is a desirable property of a time stepping scheme, as it allows the choice of time step solely based on accuracy considerations. Of particular interest are problems for which both the implicit and explicit parts of the ImEx splitting are stiff. Such splittings can arise, for example, in variable-coefficient problems, or the incompressible Navier-Stokes equations. To characterize the new ImEx schemes, an unconditional stability region is introduced, which plays a role analogous to that of the stability region in conventional multistep methods. Moreover, computable quantities (such as a numerical range) are provided that guarantee an unconditionally stable scheme for a proposed implicit-explicit matrix splitting. The new approach is illustrated with several examples. Coefficients of the new schemes up to fifth order are provided.