Symplectic integrators for second-order linear non-autonomous equations

DOI10.1016/j.cam.2017.03.028zbMath1376.65147arXiv1702.04768OpenAlexW2590676912MaRDI QIDQ1676022

Fernando Casas, Philipp Bader, Nikita Kopylov, Enrique Ponsoda, Sergio Blanes

Publication date: 3 November 2017

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.04768

zbMATH Keywords

numerical experimentsymplectic integratorsMagnus expansionsecond-order linear differential equationsnon-autonomousmatrix Hill's equation

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (6)

A Lie group integrator to solve the hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet ⋮ A fast and efficient computation method for reflective diffraction simulations ⋮ Novel symplectic integrators for the Klein-Gordon equation with space- and time-dependent mass ⋮ Symplecticness conditions of some low order partitioned methods for non-autonomous Hamiltonian systems ⋮ Solving the wave equation with multifrequency oscillations ⋮ An efficient numerical treatment for the asymptotic behaviour of the nonlinear Airy-type problems

Cites Work

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• Efficient and accurate algorithms for computing matrix trigonometric functions
• Efficient numerical integration of \(N\)th-order non-autonomous linear differential equations
• Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods
• Splitting methods in the numerical integration of non-autonomous dynamical systems
• Symplectic integrators for the matrix Hill equation
• A Concise Introduction to Geometric Numerical Integration
• Solving the Pertubed Quantum Harmonic Oscillator in Imaginary Time Using Splitting Methods with Complex Coefficients
• Splitting methods for non-autonomous linear systems
• Computations in a free Lie algebra
• On the solution of linear differential equations in Lie groups
• Collocation and Relaxed Collocation for the Fer and the Magnus Expansions
• New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously
• Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential
• Geometric Numerical Integration
• On the exponential solution of differential equations for a linear operator

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