Lobatto IIIA methods, direct transcription, and DAEs with delays

• Published in: Numerical algorithms Vol. 69; no. 2; pp. 291 - 300
• Main Authors: Betts, John T., Campbell, Stephen L., Thompson, Karmethia
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-06-2015; Springer Nature B.V
• Subjects: Algebra; Algorithms; Computer Science; Differential equations; Interpolation; Numeric Computing; Numerical Analysis; Original Paper; Theory of Computation; Numerical discretizations; Stability; Delays; Direct transcription; Optimal control
• ISSN: 1017-1398; 1572-9265
• DOI: 10.1007/s11075-014-9896-y

Recent results in the literature have shown that LobattoIIIA methods may have some undesirable stability properties when used to numerically integrate differential algebraic equations (DAEs) which have delays. In these studies Lagrange interpolation was used to compute the delayed terms. Here we show that this undesirable behavior of LobattoIIIA methods reported in the literature is tied to the use of Lagrange interpolation and their use in an ODE integrator. With these and other natural interpolations some LobattoIIIA methods do not exhibit this undesirable behavior when used within a direct transcription framework.