Solving differential-algebraic equations by Taylor series. II: Computing the system Jacobian

DOI10.1007/s10543-006-0106-8zbMath1123.65080OpenAlexW2013758652MaRDI QIDQ878197

Nedialko S. Nedialkov, John D. Pryce

Publication date: 26 April 2007

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-006-0106-8

zbMATH Keywords

algorithmsautomatic differentiationTaylor seriesstructural analysisdifferential-algebraic equations(DAE)

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Implicit ordinary differential equations, differential-algebraic equations (34A09) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for differential-algebraic equations (65L80)

Related Items

Structural Analysis for the Design of Reliable Controllers and State Estimators for Uncertain Dynamical Systems ⋮ A Simple Method for Quasilinearity Analysis of DAEs ⋮ Interval arithmetic techniques for the design of controllers for nonlinear dynamical systems with applications in mechatronics. II ⋮ Convergent power series of \(\operatorname{sech}(x)\) and solutions to nonlinear differential equations ⋮ Symbolic-Numeric Methods for Improving Structural Analysis of Differential-Algebraic Equation Systems ⋮ One-step 9-stage Hermite-Birkhoff-Taylor DAE solver of order 10 ⋮ Detecting structures in differential algebraic equations: computational aspects ⋮ An Hermite-Obreschkoff method for stiff high-index DAE ⋮ A new algorithm for index determination in DAEs using algorithmic differentiation ⋮ Status of the differential transformation method ⋮ High-Order Adaptive Time Stepping for the Incompressible Navier--Stokes Equations ⋮ Automatic implementation of the numerical Taylor series method: a \textsc{Mathematica} and \textsc{Sage} approach ⋮ Breaking the limits: The Taylor series method ⋮ How AD can help solve differential-algebraic equations ⋮ A numerical algorithm for solving higher-order nonlinear BVPs with an application on fluid flow over a shrinking permeable infinite long cylinder ⋮ Parameter range reduction from partial data in systems of differential algebraic equations ⋮ Parameter identification and observer-based control for distributed heating systems– the basis for temperature control of solid oxide fuel cell stacks ⋮ Algorithm 948

Uses Software

• ADOL-C
• FADBAD++

Cites Work

• Solving high-index DAEs by Taylor series
• Performance of the Taylor series method for ODEs/DAEs
• Solving differential-algebraic equations by Taylor series. I: Computing Taylor coefficients
• The Consistent Initialization of Differential-Algebraic Systems
• Algorithm 755: ADOL-C
• Differential--Algebraic Equations of Index 1 May Have an Arbitrarily High Structural Index
• A simple structural analysis method for DAEs
• Unnamed Item