The method of normal splines for linear DAEs on the number semi-axis

DOI10.1016/j.apnum.2008.03.009zbMath1160.65045OpenAlexW2021361197MaRDI QIDQ1007386

J. Martínez

Publication date: 20 March 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2008.03.009

zbMATH Keywords

algorithmnumerical examplesdifferential-algebraic equationscollocationreproducing kernelequations on the semi-axisHilbert-Sobolev spacenormal splinesvariable degeneracy

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical methods for differential-algebraic equations (65L80) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

Spline reproducing kernels on \(\mathbb{R}\) and error bounds for piecewise smooth LBV problems, A parametrization method for the numerical solution of singular differential equations, Numerical solution of differential-algebraic equations using the spline collocation-variation method

Uses Software

• MATSLISE
• COLNEW
• RODAS

Cites Work

• Solution of the Schrödinger equation over an infinite integration interval by perturbation methods, revisited
• The method of normal splines for linear implicit differential equations of second order
• A parametrization method for the numerical solution of singular differential equations
• The solution of Cauchy's problem for a system of second-order linear differential equations, unsolvable for the highest derivative
• Numerical solution of an equation with a small parameter on an infinite interval
• Iterative regularization based on singular analysis
• The parameterization method in optimal control problems and differential-algebraic equations
• Development of the Normal Spline Method for Linear Integro-Differential Equations
• Solvability of Boundary Value Problems for Systems of Singular Differential-Algebraic Equations
• Collocation Software for Boundary Value Differential-Algebraic Equations
• DUALITY OF CONVEX FUNCTIONS AND EXTREMUM PROBLEMS
• Theory of Reproducing Kernels
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item