Linear-implicit strong schemes for Itô-Galerkin approximations of stochastic PDEs.
Kloeden, P.E., Shott, S. (2001)
Journal of Applied Mathematics and Stochastic Analysis
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Kloeden, P.E., Shott, S. (2001)
Journal of Applied Mathematics and Stochastic Analysis
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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...
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...
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...
Mohamed El Makrini, Benjamin Jourdain, Tony Lelièvre (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
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The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a fixed number of random walkers evolving according to a stochastic differential equation discretized in time. We allow stochastic reconfigurations of the walkers to reduce the discrepancy between the weights that they carry. On a simple one-dimensional example,...
Accardi, L., Kozyrev, S.V. (2004)
Discrete Dynamics in Nature and Society
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