A new projector based decoupling of linear DAEs for monitoring singularities

• Published in: Numerical algorithms Vol. 73; no. 2; pp. 535 - 565
• Main Authors: Schwarz, Diana Estévez, Lamour, René
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2016; Springer Nature B.V
• Subjects: Algebra; Algorithms; Computer Science; Decoupling; Derivatives; Differential equations; Differentiation; Mathematical analysis; Monitoring; Numeric Computing; Numerical Analysis; Original Paper; Projectors; Robustness (mathematics); Singularities; Singularity (mathematics); Theory of Computation; 34C05; MNA; Singular value; Hessenberg form; DAE; Index; Kronecker canonical form; Modified nodal analysis; Differential-algebraic equation; Golden ratio; 34A09; Projector-based analysis; 65L80; Condition number; Derivative array
• ISSN: 1017-1398; 1572-9265
• DOI: 10.1007/s11075-016-0107-x

For higher index differential-algebraic equations (DAEs) some components of the solution depend on derivatives of the right-hand side. In this context, two main results are pointed out here. On the one hand, a description of the different types of undifferentiated components involved in the DAE is obtained by a projector-based decoupling. To this end, we define a new decoupling based on the number of inherent differentiations of the right-hand side that are required to determine each component. On the other hand, we introduce characteristic values that characterize the robustness of our numerically determined index-classification and decoupling as well as a meaningful indicator that permit the diagnosis of singular points.