Generalized ROW-type methods for solving semi-explicit DAEs of index-1

详细信息    查看全文

• 作者：T. Jax ; ^{tim.jax@h-brs.de} ; G. Steinebach ^{gerd.steinebach@h-brs.de}
• 关键词：Rosenbrock methods ; W methods ; Differential&ndash ; algebraic equations ; Order conditions ; Approximated Jacobian
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：316
• 期：Complete
• 页码：213-228
• 全文大小：751 K
• 卷排序：316

文摘

A new type of Rosenbrock–Wanner (ROW) methods for solving semi-explicit DAEs of index-1 is introduced. The scheme considers arbitrary approximations to Jacobian entries resulting for the differential part and thus corresponds to a first attempt of applying W methods to DAEs. Besides, it is a generalized class covering many ROW-type methods known from literature. Order conditions are derived by a consistent approach that combines theories of ROW methods with exact Jacobian for DAEs (Roche, 1988) and W methods with arbitrary Jacobian for ODEs (Steihaug and Wolfbrandt, 1979). In this context, rooted trees based on Butcher’s theory that include a new type of vertices are used to describe non-exact differentials of the numerical solution. Resulting conditions up to order four are given explicitly, including new conditions for realizing schemes of higher order. Numerical tests emphasize the relevance of satisfying these conditions when solving DAEs together with approximations to Jacobian entries of the differential part.