Výsledky vyhledávání - "McLachlan, R."

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Homoclinic tangencies with infinitely many asymptotically stable single-round periodic solutions

Autor: Muni, S. S., McLachlan, R. I., Simpson, D. J. W.

We consider a homoclinic orbit to a saddle fixed point of an arbitrary $C^\infty$ map $f$ on $\mathbb{R}^2$ and study the phenomenon that $f$ has an infinite family of asymptotically stable, single-round periodic solutions. From classical theory, thi

Externí odkaz: http://arxiv.org/abs/2006.01405

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The use of discrete gradient methods for total variation type regularization problems in image processing

Autor: Grimm, V, McLachlan, R I, McLaren, D, Quispel, G R W, Schönlieb, C-B

Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing tasks. We pr

Externí odkaz: http://arxiv.org/abs/1603.07515

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Efficient and accurate methods for solving the time-dependent spin-1 Gross-Pitaevskii equation

Autor: Symes, L. M., McLachlan, R. I., Blakie, P. B.

Publikováno v: Phys. Rev. E 93, 053309 (2016)

We develop a numerical method for solving the spin-1 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of the spin-1 evolution equation that leads to two exactly solvable flows. We use this to implement a second-order and a four

Externí odkaz: http://arxiv.org/abs/1602.06638

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The multisymplectic diamond scheme

Autor: McLachlan, R I, Wilkins, M C

We introduce a class of general purpose linear multisymplectic integrators for Hamiltonian wave equations based on a diamond-shaped mesh. On each diamond, the PDE is discretized by a symplectic Runge--Kutta method. The scheme advances in time by fill

Externí odkaz: http://arxiv.org/abs/1402.4115

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Preserving energy resp. dissipation in numerical PDEs using the 'Average Vector Field' method

Autor: Celledoni, E., Grimm, V., McLachlan, R. I., McLaren, D. I., O'Neale, D., Owren, B., Quispel, G. R. W.

We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly. The same method, applied to PDEs with constant dissipative structure, also prese

Externí odkaz: http://arxiv.org/abs/1202.4555

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