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

DOI10.1007/s11075-017-0379-9zbMath1409.65049OpenAlexW2738910933MaRDI QIDQ1646662

René Lamour, Diana Estévez Schwarz

Publication date: 25 June 2018

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-017-0379-9

zbMATH Keywords

automatic differentiationdifferential-algebraic equationindexconsistent initial valueSQPnonlinear constrained optimizationderivative arrayDAEprojector based analysis

Mathematics Subject Classification ID

Nonlinear programming (90C30) Implicit ordinary differential equations, differential-algebraic equations (34A09) Numerical methods for differential-algebraic equations (65L80) Methods of successive quadratic programming type (90C55)

Related Items

Projected explicit and implicit Taylor series methods for DAEs, Parareal for index two differential algebraic equations, An Energy-Based, Always Index $\leq$ 1 and Structurally Amenable Electrical Circuit Model, Quadratized Taylor series methods for ODE numerical integration, A Projector Based Decoupling of DAEs Obtained from the Derivative Array, Least-Squares Collocation for Higher-Index DAEs: Global Approach and Attempts Toward a Time-Stepping Version, Singularities of the Robotic Arm DAE, InitDAE: computation of consistent values, index determination and diagnosis of singularities of DAEs using automatic differentiation in Python, Index-analysis for a method of lines discretising multirate partial differential algebraic equations, On a class of conjugate symplectic Hermite-Obreshkov one-step methods with continuous spline extension, The structural index of sensitivity equation systems

Uses Software

• GELDA
• Dymola
• DAETS
• Python
• AlgoPy
• DFVLR-SQP

Cites Work

• A new projector based decoupling of linear DAEs for monitoring singularities
• A minimal norm corrected underdetermined Gauß-Newton procedure
• Differential-algebraic equations. A projector based analysis
• Behavior of the nonunique terms in general DAE integrators
• The properties of differential-algebraic equations representing optimal control problems
• A New Software Package for Linear Differential-Algebraic Equations
• Computing the Structural Index
• The Consistent Initialization of Differential-Algebraic Systems
• The Numerical Solution of Higher Index Linear Time Varying Singular Systems of Differential Equations
• A Successive Linear Programming Approach for Initialization and Reinitialization after Discontinuities of Differential-Algebraic Equations
• Solvability of General Differential Algebraic Equations
• The computation of consistent initial values for nonlinear index-2 differential-algebraic equations
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