A new approach for computing consistent initial values and Taylor coefficients for DAEs using projector-based constrained optimization

• Published in: Numerical algorithms Vol. 78; no. 2; pp. 355 - 377
• Main Authors: Estévez Schwarz, Diana, Lamour, René
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2018; Springer Nature B.V
• Subjects: Algebra; Algorithms; Coefficients; Computer Science; Differential equations; Linear algebra; Mathematics; Numeric Computing; Numerical Analysis; Optimization; Original Paper; Quadratic programming; Theory of Computation; 65L05; Consistent initial value; Projector based analysis; 34A34; DAE; Index; Differential-algebraic equation; 34A09; Automatic differentiation; SQP; 90C30; 90C55; 65L80; 65D25; Derivative array; Nonlinear constrained optimization
• ISSN: 1017-1398; 1572-9265
• DOI: 10.1007/s11075-017-0379-9

This article describes a new algorithm for the computation of consistent initial values for differential-algebraic equations (DAEs). The main idea is to formulate the task as a constrained optimization problem in which, for the differentiated components, the computed consistent values are as close as possible to user-given guesses. The generalization to compute Taylor coefficients results immediately, whereas the amount of consistent coefficients will depend on the size of the derivative array and the index of the DAE. The algorithm can be realized using automatic differentiation (AD) and sequential quadratic programming (SQP). The implementation in Python using AlgoPy and SLSQP has been tested successfully for several higher index problems.