Implicit Riquier bases for PDAE and their semi-discretizations

DOI10.1016/j.jsc.2008.04.020zbMath1170.65075OpenAlexW2136692263MaRDI QIDQ1025399

Greg Reid, Silvana Ilie, Wenyuan Wu

Publication date: 18 June 2009

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2008.04.020

zbMATH Keywords

finite elementsstabilizationfinite differencesmethod of linesdifferential algebraic equationssemi-discretizationinitial boundary value problempartial differential algebraic equationsRiquier basessymbolic-numeric approach

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Implicit ordinary differential equations, differential-algebraic equations (34A09) Partial functional-differential equations (35R10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for differential-algebraic equations (65L80) Initial value problems for nonlinear first-order PDEs (35F25)

Related Items (3)

Efficient index reduction algorithm for large scale systems of differential algebraic equations ⋮ Polynomial cost for solving IVP for high-index DAE ⋮ Index reduction of differential algebraic equations by differential Dixon resultant

Uses Software

• PHCpack
• ObservabilityTest

Cites Work

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• Completion to involution and semidiscretisations
• Overdetermined elliptic systems
• Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time
• Algorithm 795
• Differential Elimination–Completion Algorithms for DAE and PDAE
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Simplifying numerical solution of constrained PDE systems through involutive completion
• A probabilistic algorithm to test local algebraic observability in polynomial time
• Algorithms in real algebraic geometry
• A simple structural analysis method for DAEs

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