Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations. I: Basics and ansatz function choices
From MaRDI portal
Publication:2116034
DOI10.1007/s11075-021-01140-7zbMath1484.65164OpenAlexW3167330257WikidataQ115381582 ScholiaQ115381582MaRDI QIDQ2116034
Publication date: 16 March 2022
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11075-021-01140-7
Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical methods for differential-algebraic equations (65L80) General theory for ordinary differential equations (34A99) Numerical solution of ill-posed problems involving ordinary differential equations (65L08)
Related Items
A numerical algorithm for solving index-1 weakly singular integral-algebraic equations with non-smooth solutions ⋮ On the sensitivity of implementations of a least-squares collocation method for linear higher-index differential-algebraic equations
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Lebesgue functions and Lebesgue constants in polynomial interpolation
- Differential-algebraic equations. A projector based analysis
- Least-squares collocation for linear higher-index differential-algebraic equations
- Optimally scaled and optimally conditioned vandermonde and Vandermonde-like matrices
- The condition of Vandermonde-like matrices involving orthogonal polynomials
- Lower bounds for the condition number of Vandermonde matrices
- Two results on polynomial interpolation in equally spaced points
- Numerical mathematics. I.
- Constraint preserving integrators for general nonlinear higher index DAEs
- The condition number of real Vandermonde, Krylov and positive definite Hankel matrices
- Gauss-Radau formulae for Jacobi and Laguerre weight functions
- Backward stability of Clenshaw's algorithm
- 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
- Boundary-Value Problems for Differential-Algebraic Equations: A Survey
- Algorithm 915, SuiteSparseQR
- A Remark on Stirling's Formula
- Direct Methods for Sparse Linear Systems
- Differential-Algebraic Equations from a Functional-Analytic Viewpoint: A Survey
- Collocation methods for index 1 DAEs with a singularity of the first kind
- A New Basis Implementation for a Mixed Order Boundary Value ODE Solver
- Abscissas and Weight Coefficients for Lobatto Quadrature
- Collocation Software for Boundary Value Differential-Algebraic Equations
- Spectral Methods in MATLAB
- Numerische Mathematik 1
- Least-squares collocation for higher-index linear differential-algebraic equations: Estimating the instability threshold
- A Practical Guide to Pseudospectral Methods
- Calculation of the principal values, weights and nodes of the gauss quadrature formulae of integrals
- Calculation of Gauss Quadrature Rules
- High-order Gauss-Lobatto formulae
- Rounding error bounds for the Clenshaw and Forsythe algorithms for the evaluation of orthogonal polynomial series
