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

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 a...

Full description

Saved in:
Bibliographic Details
Published in:Numerical algorithms 2018-06, Vol.78 (2), p.355-377
Main Authors: Estévez Schwarz, Diana, Lamour, René
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Coefficients
Computer Science
Differential equations
Linear algebra
Mathematics
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Quadratic programming
Theory of Computation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-017-0379-9