Computing the structural index
SIAM Journal on Algebraic and Discrete Methods
A general form for solvable linear time varying singular systems of differential equations
SIAM Journal on Mathematical Analysis
The consistent intialization of differential-algebraic systems
SIAM Journal on Scientific and Statistical Computing
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
On Asymptotics in Case of Linear Index-2 Differential-Algebraic Equations
SIAM Journal on Numerical Analysis
Solving Ordinary Differential Equations Using Taylor Series
ACM Transactions on Mathematical Software (TOMS)
Differential--Algebraic Equations of Index 1 May Have an Arbitrarily High Structural Index
SIAM Journal on Scientific Computing
High-Order Stiff ODE Solvers via Automatic Differentiation and Rational Prediction
WNAA '96 Proceedings of the First International Workshop on Numerical Analysis and Its Applications
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Differential-Algebraic Systems: Analytical Aspects and Circuit Applications
Differential-Algebraic Systems: Analytical Aspects and Circuit Applications
| Hi-index | 7.29 |
Automatic (or Algorithmic) Differentiation (AD) opens new possibilities to analyze and solve DAEs by projector based methods. In this paper, we present a new approach to compute consistent initial values and integrate DAEs up to index two, considering the nonlinear DAE in each time-step as a nonlinear system of equations for Taylor expansions. These systems will be solved by the Newton-Kantorowitsch method, whereas the resulting linear systems are decoupled using the splitting techniques related to the tractability index concept. This approach provides a description of the inherent ODE that allows an application of the classical Taylor series method to the integration of initial value problems. Linear and nonlinear DAEs with index up to two are examined and solved numerically.