(Spectral) Chebyshev collocation methods for solving differential equations
DOI10.1007/s11075-022-01482-wzbMath1523.65100arXiv2205.15266OpenAlexW4315777346MaRDI QIDQ6109892
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro
Publication date: 31 July 2023
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2205.15266
Chebyshev polynomialsLegendre polynomialsHamiltonian boundary value methodsChebyshev collocation methodsHBVMs
Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)
Cites Work
- Unnamed Item
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- A simple framework for the derivation and analysis of effective one-step methods for ODEs
- A note on the efficient implementation of Hamiltonian BVMs
- A class of collocation methods for numerical integration of initial value problems
- Stability of Chebyshev collocation methods
- A general framework for solving differential equations
- Analysis of spectral Hamiltonian boundary value methods (SHBVMs) for the numerical solution of ODE problems
- Spectrally accurate space-time solution of Manakov systems
- High-order energy-conserving line integral methods for charged particle dynamics
- A note on the continuous-stage Runge-Kutta(-Nyström) formulation of Hamiltonian boundary value methods (HBVMs)
- Line integral solution of differential problems
- Spectrally accurate space-time solution of Hamiltonian PDEs
- On the effectiveness of spectral methods for the numerical solution of multi-frequency highly oscillatory Hamiltonian problems
- An algebraic approach to invariant preserving integators: the case of quadratic and Hamiltonian invariants
- Arbitrarily high-order energy-conserving methods for Poisson problems
- A Concise Introduction to Geometric Numerical Integration
- Symplectic Runge--Kutta Schemes for Adjoint Equations, Automatic Differentiation, Optimal Control, and More
- Line Integral Methods for Conservative Problems
- Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
- Simulating Hamiltonian Dynamics
- Symplectic Geometric Algorithms for Hamiltonian Systems
- Geometric integration using discrete gradients
- Energy-preserving Runge-Kutta methods
- Spectrally accurate energy‐preserving methods for the numerical solution of the “good” Boussinesq equation
- Geometric Numerical Integration
- s-stage Trapezoidal Methods for the Conservation of Hamiltonian Functions of Polynomial Type
- Functionally Fitted Energy-Preserving Methods for Solving Oscillatory Nonlinear Hamiltonian Systems
- B-Series
- A method for global approximation of the initial value problem
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