Weighted least squares collocation methods

Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Cites Work

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A simple framework for the derivation and analysis of effective one-step methods for ODEs
Least-squares collocation for linear higher-index differential-algebraic equations
A note on the efficient implementation of Hamiltonian BVMs
A general framework for solving differential equations
Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations. I: Basics and ansatz function choices
Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations. II: The discrete least-squares problem
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
Line integral solution of differential problems
Efficient implementation of Gauss collocation and Hamiltonian boundary value methods
Line Integral Methods for Conservative Problems
Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
On Spline Basis Selection for Solving Differential Equations
Discrete Least Squares Approximations for Ordinary Differential Equations
A New Basis Implementation for a Mixed Order Boundary Value ODE Solver
Collocation Software for Boundary Value Differential-Algebraic Equations
Least-squares collocation for higher-index linear differential-algebraic equations: Estimating the instability threshold
Geometric Numerical Integration

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