Boundary-Value Problems for Differential-Algebraic Equations: A Survey

DOI10.1007/978-3-319-22428-2_4zbMath1343.65102OpenAlexW2277662881MaRDI QIDQ2795642

Roswitha März, René Lamour, Ewa B. Weinmüller

Publication date: 22 March 2016

Published in: Surveys in Differential-Algebraic Equations III (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-22428-2_4

zbMATH Keywords

collocation methodfinite difference methodnumerical methodsLyapunov stabilityboundary value problemserror estimationwell-posednessdifferential-algebraic equationshooting methodsNewton-Kantorovich methodperiodical solutionFloquet exponentindex-1index-2Abramov transfer method

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Implicit ordinary differential equations, differential-algebraic equations (34A09) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for differential-algebraic equations (65L80) Linear boundary value problems for ordinary differential equations (34B05) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items

Acceleration of implicit schemes for large systems of nonlinear differential-algebraic equations, New answers to an old question in the theory of differential-algebraic equations: essential underlying ODE versus inherent ODE, Least-Squares Collocation for Higher-Index DAEs: Global Approach and Attempts Toward a Time-Stepping Version, Convergence analysis of least-squares collocation methods for nonlinear higher-index differential-algebraic equations, A reliable direct numerical treatment of differential-algebraic equations by overdetermined collocation: an operator approach, Least-squares collocation for higher-index linear differential-algebraic equations: Estimating the instability threshold, Solving higher index DAE optimal control problems, Least-squares collocation for linear higher-index differential-algebraic equations, Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations. I: Basics and ansatz function choices

Uses Software

• COLNEW
• COLSYS
• Sbvp

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