[PDF] Top 20 Multiscale Model Reduction Methods for Deterministic and Stochastic Partial Differential Equations
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Multiscale Model Reduction Methods for Deterministic and Stochastic Partial Differential Equations
... fewer equations and unknown vari- ables, which can be solved much more quickly than the original ...‘model reduction’ and apply it to the multiscale ...effective equations are not as ... See full document
118
Quasilinear Stochastic Partial Differential Equations
... Quasilinear stochastic PDE’s occur in applications such as the stochastic Navier-Stokes equation for which there is a complete answer to existence and uniqueness of ...The stochastic term in each of ... See full document
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Stochastic partial differential equations with coefficients depending on VaR
... the stochastic analysis for irregular functionals of time ...the deterministic analysis for regular (smooth) functionals of time, due to the Itˆ o’s formula for the Stratonovich ... See full document
98
Discretisations of rough stochastic partial differential equations
... Stochastic PDEs are used to describe many physical, biological and econom- ical systems which, in contrast to deterministic systems, are subject to a random “noise”, see e.g. [BS95, GLP99, HL09]. This ... See full document
166
The Osgood condition for stochastic partial differential equations
... the equations are defined on the whole ...the deterministic setting, similar phenomenon arises; see for instance [16] where the exponential reaction-diffusion is ... See full document
19
Adaptive Methods Exploring Intrinsic Sparse Structures of Stochastic Partial Differential Equations
... by stochastic forces are considered, which can be considered the simplest ...with deterministic velocity and random initial ...by stochastic force as an example of a nonlinear PDE driven by ... See full document
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Path Integral Methods for Stochastic Differential Equations
... neuroscience, stochastic differential equations (SDE) have been uti- lized to model stochastic phenomena that range in scale from molecular transport in neurons, to neuronal firing, to ... See full document
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Multiscale Geometric Integration of Deterministic and Stochastic Systems
... Impulse methods have been mollified [109, 240] to gain extra stability and accuracy while the mollified method remains ...impulse methods and Gautschi-type integrators [143] (reversible but not necessarily ... See full document
315
Numerical methods for simulation of stochastic differential equations
... ignored stochastic effects because of difficulty in so- lution. But now, stochastic differential equations (SDEs) play a significant role in many departments of science and industry because of their ... See full document
10
Multiscale Methods for Elliptic Partial Differential Equations and Related Applications
... the multiscale nature of formation properties, not only is a complete analysis of these problems extremely difficult, but also numerical solvers require an excessive amount of CPU time and ...study ... See full document
119
Stochastic vs. deterministic models for systems with delays
... to model physical and biological processes ...population stochastic systems, in such models one often wishes to know whether or not the stochastic system can be approx- imated by a ... See full document
6
Numerical methods for Stochastic differential equations: two examples
... Stochastic Differential Equations (SDE in short) constrained in law have been introduced recently in their backward form by Briand, Elie and Hu in ...being deterministic, satisfying on [0, T ... See full document
13
On some properties of a class of fractional stochastic heat equations
... In this section, we will indicate how to get existence and uniqueness of random field solutions for the equations studied in this paper. We will focus on the coloured driven equation. We will following a standard ... See full document
24
A stochastic differential equation SIS epidemic model with two correlated Brownian motions
... The previous section has already provided us with enough evidence that our model has a unique posi- tive bounded solution. However, we do not know under what circumstances the disease will die out or persist and ... See full document
13
Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations
... to effects quadratic in the noise amplitude σ, and seeks the normal form where the evolution involves no convolutions. Also, transform the quadratic noise in the evolution. Throughout we adopt the Stratonovich ... See full document
21
Similarity Reduction of Nonlinear Partial Differential Equations
... nonlinear partial differential ...similarity reduction of nonlinear partial differential equations is to use classical Lie approach ... See full document
11
Reichenbach, Tobias (2008): Dynamic patterns of biological systems: From transport to species diversity. Dissertation, LMU München: Fakultät für Physik
... left of the domain wall position, both spin states have comparable densities, corresponding to low (or vanishing) polarization. To the right, the density difference jumps to a high value, such that the system is ... See full document
167
Optimal rate of convergence for stochastic Burgers type equations
... In Sect. 2 we review the theories of rough paths and controlled rough paths. Section 3 is devoted to the results obtained in [18]. In particular, here we provide a notion of solution and the existence and uniqueness ... See full document
37
Structure preserving stochastic Runge–Kutta–Nyström methods for nonlinear second order stochastic differential equations with multiplicative noise
... The second-order SDE (1.5) describes the position of a particle subject to deterministic forcing f (y) and random forcing ξ (t) [21]. By introducing a new variable z(t) = y(t), (1.5) ˙ can be written as a pair of ... See full document
18
Supremum estimates for degenerate, quasilinear stochastic partial differential equations
... In the following we will briefly comment on existing literature on the regularity of solutions to stochastic porous media equations. The existence of strong solutions (i.e. | u | m − 1 u ∈ L 2 ((0, T ) ; H ... See full document
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