A reliable direct numerical treatment of differential-algebraic equations by overdetermined collocation: an operator approach

DOI10.1016/j.cam.2019.112520zbMath1458.65105OpenAlexW2978973956WikidataQ115359779 ScholiaQ115359779MaRDI QIDQ2223825

Michael Hanke, Roswitha März

Publication date: 3 February 2021

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2019.112520

zbMATH Keywords

essentially ill-posed problemleast-squares problemdifferential-algebraic operatorhigher-order differential-algebraic equationoverdetermined polynomial collocation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical methods for differential-algebraic equations (65L80)

Related Items (3)

Convergence analysis of least-squares collocation methods for nonlinear higher-index differential-algebraic equations ⋮ On the sensitivity of implementations of a least-squares collocation method 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

Cites Work

• Differential-algebraic equations. A projector based analysis
• Least-squares collocation for linear higher-index differential-algebraic equations
• Transformation of high order linear differential-algebraic systems to first order
• Application of matrix polynomials to the analysis of linear differential-algebraic equations of higher order
• Projected collocation for higher-order higher-index differential- algebraic equations
• Boundary-Value Problems for Differential-Algebraic Equations: A Survey
• Differential-Algebraic Equations from a Functional-Analytic Viewpoint: A Survey
• A New Basis Implementation for a Mixed Order Boundary Value ODE Solver
• The Numerical Solution of Higher Index Linear Time Varying Singular Systems of Differential Equations
• Collocation Software for Boundary Value Differential-Algebraic Equations
• Least-squares collocation for higher-index linear differential-algebraic equations: Estimating the instability threshold
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