scholarly journals Weak Error Analysis of Numerical Methods for Stochastic Models of Population Processes

2012 ◽  
Vol 10 (4) ◽  
pp. 1493-1524 ◽  
Author(s):  
David F. Anderson ◽  
Masanori Koyama
Keyword(s):  
Numerical Methods ◽  
Error Analysis ◽  
Stochastic Models ◽  
Population Processes ◽  
Weak Error

scholarly journals Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 155
Author(s):  
Antonio Barrera ◽  
Patricia Román-Román ◽  
Francisco Torres-Ruiz
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Maximum Likelihood ◽  
Numerical Methods ◽  
Stochastic Models ◽  
Maximum Likelihood Method ◽  
Diffusion Processes ◽  
Oscillatory Behavior ◽  
Likelihood Method ◽  
Systems Of Equations

Stochastic models based on deterministic ones play an important role in the description of growth phenomena. In particular, models showing oscillatory behavior are suitable for modeling phenomena in several application areas, among which the field of biomedicine stands out. The oscillabolastic growth curve is an example of such oscillatory models. In this work, two stochastic models based on diffusion processes related to the oscillabolastic curve are proposed. Each of them is the solution of a stochastic differential equation obtained by modifying, in a different way, the original ordinary differential equation giving rise to the curve. After obtaining the distributions of the processes, the problem of estimating the parameters is analyzed by means of the maximum likelihood method. Due to the parametric structure of the processes, the resulting systems of equations are quite complex and require numerical methods for their resolution. The problem of obtaining initial solutions is addressed and a strategy is established for this purpose. Finally, a simulation study is carried out.

scholarly journals ‘Intractable and unsolved’: some thoughts on statistical data assimilation with uncertain static parameters

2013 ◽  
Vol 371 (1991) ◽  
pp. 20120297 ◽  
Author(s):  
Jonathan Rougier
Keyword(s):  
Numerical Methods ◽  
Data Assimilation ◽  
State Space ◽  
Stochastic Models ◽  
Environmental Science ◽  
Statistical Data ◽  
Initial Conditions ◽  
The State ◽  
Likelihood Functions ◽  
Sensitive Dependence

If you seem to be able to do data assimilation with uncertain static parameters then you are probably not working in environmental science. In this field, applications are often characterized by sensitive dependence on initial conditions and attracting sets in the state-space, which, taken together, can be a major challenge to numerical methods, leading to very peaky likelihood functions. Inherently stochastic models and uncertain static parameters increase the challenge.

scholarly journals Numerical methods for static shallow shells lying over an obstacle

2020 ◽  
Vol 85 (2) ◽  
pp. 623-652
Author(s):  
Paolo Piersanti ◽  
Xiaoqin Shen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Numerical Methods ◽  
Error Analysis ◽  
Bilinear Form ◽  
Obstacle Problem ◽  
Numerical Scheme ◽  
Shallow Shell ◽  
Element Analysis ◽  
Shallow Shells

AbstractIn this paper, a finite element analysis to approximate the solution of an obstacle problem for a static shallow shell confined in a half space is presented. To begin with, we establish, by relying on the properties of enriching operators, an estimate for the approximate bilinear form associated with the problem under consideration. Then, we conduct an error analysis and we prove the convergence of the proposed numerical scheme.

NUMERICAL ANALYSIS OF DEGENERATE CONNECTING ORBITS FOR MAPS

2004 ◽  
Vol 14 (10) ◽  
pp. 3385-3407 ◽  
Author(s):  
WOLF-JÜRGEN BEYN ◽  
THORSTEN HÜLS ◽  
YONGKUI ZOU
Keyword(s):  
Numerical Analysis ◽  
Dynamical Systems ◽  
Numerical Methods ◽  
Error Analysis ◽  
Error Estimates ◽  
Discrete Dynamical Systems ◽  
Numerical Results ◽  
Connecting Orbits ◽  
Theoretical Results ◽  
Degenerate Cases

This paper contains a survey of numerical methods for connecting orbits in discrete dynamical systems. Special emphasis is put on degenerate cases where either the orbit loses transversality or one of its endpoints loses hyperbolicity. Numerical methods that approximate the connecting orbits by finite orbit sequences are described in detail and theoretical results on the error analysis are provided. For most of the degenerate cases we present examples and numerical results that illustrate the applicability of the methods and the validity of the error estimates.

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