Displaying similar documents to “Symplectic integrators to stochastic Hamiltonian dynamical systems derived from composition methods.”

Approximation of stochastic advection diffusion equations with stochastic alternating direction explicit methods

Ali R. Soheili, Mahdieh Arezoomandan (2013)

Applications of Mathematics

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The numerical solutions of stochastic partial differential equations of Itô type with time white noise process, using stable stochastic explicit finite difference methods are considered in the paper. Basically, Stochastic Alternating Direction Explicit (SADE) finite difference schemes for solving stochastic time dependent advection-diffusion and diffusion equations are represented and the main properties of these stochastic numerical methods, e.g. stability, consistency and convergence...

On energy conservation of the simplified Takahashi-Imada method

Ernst Hairer, Robert I. McLachlan, Robert D. Skeel (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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In long-time numerical integration of Hamiltonian systems, and especially in molecular dynamics simulation, it is important that the energy is well conserved. For symplectic integrators applied with sufficiently small step size, this is guaranteed by the existence of a modified Hamiltonian that is exactly conserved up to exponentially small terms. This article is concerned with the simplified Takahashi-Imada method, which is a modification of the Störmer-Verlet method that is as easy...

Numerical solution of a stochastic model of a ball-type vibration absorber

Fischer, Cyril, Náprstek, Jiří

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The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplification, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect...

Symbolic computing in probabilistic and stochastic analysis

Marcin Kamiński (2015)

International Journal of Applied Mathematics and Computer Science

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The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the example of the well-known MAPLE system. The key theoretical methods discussed are (i) analytical derivations, (ii) the classical Monte-Carlo simulation approach, (iii) the stochastic perturbation technique, as well as (iv) some semi-analytical approaches. It is demonstrated in particular how to engage the basic symbolic tools implemented...