Journal ArticleDOI
A new class of energy-preserving numerical integration methods
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The first energy-preserving B-series numerical integration method for (ordinary) differential equations is presented and applied to several Hamiltonian systems in this article, where the first ever energy preserving B series numerical integration algorithm is presented.Abstract:
The first ever energy-preserving B-series numerical integration method for (ordinary) differential equations is presented and applied to several Hamiltonian systems. Related novel Lie algebraic results are also discussed.read more
Citations
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Journal ArticleDOI
Preserving energy resp. dissipation in numerical PDEs using the Average Vector Field method
Elena Celledoni,Volker Grimm,Robert I. McLachlan,David I. McLaren,Dion R. J. O’Neale,Brynjulf Owren,G. R. W. Quispel +6 more
TL;DR: This work gives a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly.
Posted Content
Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
TL;DR: In this article, a general framework for integrators of polynomial Hamiltonian systems is presented, based on the notion of extended collocation conditions and the definition of discrete line integral.
Energy-preserving variant of collocation methods 1
TL;DR: In this paper, a modification of collocation methods extending the "averaged vector field method" to high order was proposed, which exactly preserve energy for Hamiltonian systems, are of arbitrarily high order and fall into the class of B-series integrators.
Journal ArticleDOI
Linear energy-preserving integrators for Poisson systems
David Cohen,Ernst Hairer +1 more
TL;DR: In this article, a new class of numerical integrators for Hamiltonian systems with non-canonical structure matrix was proposed, which exactly preserve energy, are invariant with respect to linear transformations, and have arbitrarily high order.
Journal ArticleDOI
Arbitrary-Order Trigonometric Fourier Collocation Methods for Multi-Frequency Oscillatory Systems
TL;DR: The trigonometric Fourier collocation methods are significantly more efficient in comparison with alternative approaches that have previously appeared in the literature and allow for arbitrary high-order symplectic methods to deal with a special class of systems of second-order ODEs in an efficient way.
References
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Book
Geometric numerical integration
TL;DR: This work considers the semi-Lagrangian discontinuous Galerkin method for the Vlasov-Poisson system and discusses the performance of this method and compares it to cubic spline interpolation, where appropriate.
Journal ArticleDOI
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
TL;DR: The Euler Method and its Generalizations Analysis of Runge-Kutta Methods General Linear Methods Bibliography.