Jacobian reuse in explicit integrators for higher index DAEs

被引:7
作者
Campbell, SL
Zhong, YC
机构
[1] Department of Mathematics, North Carolina State University, Raleigh
基金
美国国家科学基金会;
关键词
differential algebraic equation; DAE; numerical methods;
D O I
10.1016/S0168-9274(97)00052-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Systems F(y', y, t) = 0 with F-y' identically singular are known as differential algebraic equations (DAEs) and occur in a variety of applications. The index nu is one measure of numerical difficulty. Most numerical methods for DAEs either require special structure or low index. Two alternative approaches have been proposed for numerically integrating more general higher index DAEs. This paper examines some of the mathematical issues involved in the efficient implementation of the ''explicit integration'' method. It is first shown that the reuse of Jacobians can lead to the integration of discontinuous vector fields. It is then proven that these discontinuous fields can be successfully integrated. Computational examples back up the theory. A comparison to a standard integrator on an index three control problem illustrates that while the explicit approach can be somewhat more expensive computationally, it can be easier to apply, and does not suffer from order reduction in the higher index variables. (C) 1997 Elsevier Science B.V.
引用
收藏
页码:391 / 412
页数:22
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