Exponential collocation methods for conservative or dissipative systems
DOI10.1016/j.cam.2019.04.015zbMath1418.65093arXiv1712.07830OpenAlexW2891511814WikidataQ115581032 ScholiaQ115581032MaRDI QIDQ2315819
Publication date: 26 July 2019
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1712.07830
Lyapunov functionfinite element methodscollocation methodsfirst integralexponential integratorsenergy-preserving algorithms
Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A derivation of energy-preserving exponentially-fitted integrators for Poisson systems
- Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations
- Discrete gradient methods have an energy conservation law
- A simple framework for the derivation and analysis of effective one-step methods for ODEs
- An energy-preserving exponentially-fitted continuous stage Runge-Kutta method for Hamiltonian systems
- Linear energy-preserving integrators for Poisson systems
- ERKN integrators for systems of oscillatory second-order differential equations
- Energy-preserving integrators and the structure of B-series
- A class of explicit multistep exponential integrators for semilinear problems
- Symmetric exponential integrators with an application to the cubic Schrödinger equation
- Projection methods preserving Lyapunov functions
- Implementation of exponential Rosenbrock-type integrators
- Arbitrary-order functionally fitted energy-diminishing methods for gradient systems
- Functionally-fitted energy-preserving integrators for Poisson systems
- On the performance of exponential integrators for problems in magnetohydrodynamics
- Energy-conserving Hamiltonian boundary value methods for the numerical solution of the Korteweg-de Vries equation
- Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nyström methods
- Exponential Runge-Kutta methods for parabolic problems.
- A Gautschi-type method for oscillatory second-order differential equations
- Think globally, act locally: Solving highly-oscillatory ordinary differential equations
- A new high precision energy-preserving integrator for system of oscillatory second-order differential equations
- Inherently energy conserving time finite elements for classical mechanics
- A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator
- Efficient energy-preserving integrators for oscillatory Hamiltonian systems
- Time finite element methods: a unified framework for numerical discretizations of ODEs
- Efficient implementation of RKN-type Fourier collocation methods for second-order differential equations
- Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems
- New methods for oscillatory systems based on ARKN methods
- A class of explicit exponential general linear methods
- Numerical energy conservation for multi-frequency oscillatory differential equations
- A note on energy conservation for Hamiltonian systems using continuous time finite elements
- Finite element approximation of an Allen-Cahn/Cahn-Hilliard system
- Exponential Integrators Preserving First Integrals or Lyapunov Functions for Conservative or Dissipative Systems
- Exponential integrators
- Line Integral Methods for Conservative Problems
- Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
- Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
- Long-Time-Step Methods for Oscillatory Differential Equations
- Geometric integration using discrete gradients
- Runge-Kutta Methods for Parabolic Equations and Convolution Quadrature
- On Krylov Subspace Approximations to the Matrix Exponential Operator
- Exponential Integrators for Large Systems of Differential Equations
- Unified Approach to Hamiltonian Systems, Poisson Systems, Gradient Systems, and Systems with Lyapunov Functions or First Integrals
- Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations
- Exponential Fourier Collocation Methods for Solving First-Order Differential Equations
- Structure-Preserving Algorithms for Oscillatory Differential Equations
- Energy- and Quadratic Invariants--Preserving Integrators Based upon Gauss Collocation Formulae
- Projected explicit lawson methods for the integration of Schrödinger equation
- Trees, B-series and exponential integrators
- Spectrally accurate energy‐preserving methods for the numerical solution of the “good” Boussinesq equation
- Exponential Rosenbrock-Type Methods
- Energy-diminishing integration of gradient systems
- The minimal stage, energy preserving Runge–Kutta method for polynomial Hamiltonian systems is the averaged vector field method
- A new class of energy-preserving numerical integration methods
- Error analysis of exponential integrators for oscillatory second-order differential equations
- Geometric Numerical Integration
- B-series and Order Conditions for Exponential Integrators
- Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
- Functionally Fitted Energy-Preserving Methods for Solving Oscillatory Nonlinear Hamiltonian Systems
- Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
- Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: Nonsmooth-data error estimates and applications to long-time behaviour
- Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems