Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time

DOI10.1007/s11075-005-9007-1zbMath1095.65081OpenAlexW2078578895MaRDI QIDQ2492797

Greg Reid, Silvana Ilie, Robert M. Corless

Publication date: 14 June 2006

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

Full work available at URL: https://doi.org/10.1007/s11075-005-9007-1

zbMATH Keywords

complexityinitial value problemsdifferential algebraic equationsTaylor seriesTaylor series methodadaptive step-size control

Mathematics Subject Classification ID

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) Complexity and performance of numerical algorithms (65Y20) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (5)

Adaptivity and computational complexity in the numerical solution of ODEs ⋮ Polynomial cost for solving IVP for high-index DAE ⋮ Implicit Riquier bases for PDAE and their semi-discretizations ⋮ Exact bivariate polynomial factorization over \(\mathbb Q\) by approximation of roots ⋮ Computing real witness points of positive dimensional polynomial systems

Uses Software

• Simulink
• Ode15s
• ddesd

Cites Work

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• A new error-control for initial value solvers
• Solving high-index DAEs by Taylor series
• Some recent advances in validated methods for IVPs for ODEs
• Solving ODEs and DDEs with residual control
• Continuous numerical methods for ODEs with defect control
• A new view of the computational complexity of IVP for ODE
• Automatic control and adaptive time-stepping
• Solving differential-algebraic equations by Taylor series. I: Computing Taylor coefficients
• Solving Ordinary Differential Equations Using Taylor Series
• Fast Multiple-Precision Evaluation of Elementary Functions
• Introduction to Numerical Continuation Methods
• Solving Index-1 DAEs in MATLAB and Simulink
• An elementary solution of a minimax problem arising in algorithms for automatic mesh selection
• A simple structural analysis method for DAEs

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