A New Class of Discretization Methods for the Solution of Linear Differential-Algebraic Equations with Variable Coefficients
A New Class of Discretization Methods for the Solution of Linear Differential-Algebraic Equations with Variable Coefficients
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一类新的变系数线性微分代数方程解的离散化方法
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发表时间：
1996
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通讯作者：
V. Mehrmann
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作者：
P. Kunkel;V. Mehrmann
讨论了变系数线性微分代数方程的离散化新方法。我们引入数值方法来计算这些DAEs的局部不变量，这些不变量是由作者在之前的论文中引入的[P.]孔克尔和V. Mehrmann， J. Comput。达成。数学。， 56 (1994), pp. 225—251]。使用这些量，我们能够确定数值上的全局不变性，如奇异度指数，它推广了dae的微分指数，特别是包括未确定的解分量。在这些方法的基础上，我们得到了正则化方案，使我们能够采用通解方法。通过若干数值算例对新方法进行了验证。
We discuss new discretization methods for linear differential-algebraic equations (DAEs) with variable coefficients. We introduce numerical methods to compute the local invariants of such DAEs that were introduced by the authors in a previous paper [P. Kunkel and V. Mehrmann, J. Comput. Appl. Math., 56 (1994), pp. 225--251]. Using these quantities we are able to determine numerically global invariances like the strangeness index, which generalizes the differentiation index for DAEs that in particular include undetermined solution components. Based on these methods we then obtain regularization schemes, which allow us to employ general solution methods. The new methods are tested on a number of numerical examples.