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Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology

J. B. Burie, A. Calonnec, A. Ducrot (2010)

Mathematical Modelling of Natural Phenomena

We investigate the structure of travelling waves for a model of a fungal disease propagating over a vineyard. This model is based on a set of ODEs of the SIR-type coupled with two reaction-diffusion equations describing the dispersal of the spores produced by the fungus inside and over the vineyard. An estimate of the biological parameters in the model suggests to use a singular perturbation analysis. It allows us to compute the speed and the profile of the travelling waves. The analytical results...

Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting using Variational Iteration Method

Barari, A., Ghotbi, Abdoul R., Omidvar, M., Ganji, D. D. (2009)

Serdica Journal of Computing

Due to wide range of interest in use of bio-economic models to gain insight into the scientific management of renewable resources like fisheries and forestry,variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting.The results are compared with the results obtained by Adomian decomposition method and reveal that VIM is very effective and convenient for solving nonlinear differential equations.

Some applications of probability generating function based methods to statistical estimation

Manuel L. Esquível (2009)

Discussiones Mathematicae Probability and Statistics

After recalling previous work on probability generating functions for real valued random variables we extend to these random variables uniform laws of large numbers and functional limit theorem for the empirical probability generating function. We present an application to the study of continuous laws, namely, estimation of parameters of Gaussian, gamma and uniform laws by means of a minimum contrast estimator that uses the empirical probability generating function of the sample. We test the procedure...

Some tracks in air pollution modelling and simulation.

Bruno Sportisse, Jaouad Boutahar, Edouard Debry, Denis Quélo, Karine Sartelet (2002)

RACSAM

In this article we discuss some issues related to Air Pollution modelling (as viewed by the authors): subgrid parametrization, multiphase modelling, reduction of high dimensional models and data assimilation. Numerical applications are given with POLAIR, a 3D numerical platform devoted to modelling of atmospheric trace species.

Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs

Abdellah Chkifa, Albert Cohen, Ronald DeVore, Christoph Schwab (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The numerical approximation of parametric partial differential equations is a computational challenge, in particular when the number of involved parameter is large. This paper considers a model class of second order, linear, parametric, elliptic PDEs on a bounded domain D with diffusion coefficients depending on the parameters in an affine manner. For such models, it was shown in [9, 10] that under very weak assumptions on the diffusion coefficients, the entire family of solutions to such equations...

Sparse finite element methods for operator equations with stochastic data

Tobias von Petersdorff, Christoph Schwab (2006)

Applications of Mathematics

Let A V → V ' be a strongly elliptic operator on a d -dimensional manifold D (polyhedra or boundaries of polyhedra are also allowed). An operator equation A u = f with stochastic data f is considered. The goal of the computation is the mean field and higher moments ℳ 1 u ∈ V , ℳ 2 u ∈ V ⊗ V , ... , ℳ k u ∈ V ⊗ ⋯ ⊗ V of the solution. We discretize the mean field problem using a FEM with hierarchical basis and N degrees of freedom. We present a Monte-Carlo algorithm and a deterministic algorithm for the approximation of the moment ℳ k u for k ≥ 1 . The key tool...

Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains

Petru A. Cioica, Stephan Dahlke, Stefan Kinzel, Felix Lindner, Thorsten Raasch, Klaus Ritter, René L. Schilling (2011)

Studia Mathematica

We use the scale of Besov spaces B τ , τ α ( ) , 1/τ = α/d + 1/p, α > 0, p fixed, to study the spatial regularity of solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains ⊂ ℝ. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.

Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction

Tomáš Mrkvička, François Goreaud, Joël Chadoeuf (2011)

Kybernetika

We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory...

Spatiotemporal Dynamics in a Spatial Plankton System

R. K. Upadhyay, W. Wang, N. K. Thakur (2010)

Mathematical Modelling of Natural Phenomena

In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a condition for diffusive instability of a locally stable equilibrium. Furthermore, we present a theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially...

Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites

T. Dhirasakdanon, H. R. Thieme (2010)

Mathematical Modelling of Natural Phenomena

For an SI type endemic model with one host and two parasite strains, we study the stability of the endemic coexistence equilibrium, where the host and both parasite strains are present. Our model, which is a system of three ordinary differential equations, assumes complete cross-protection between the parasite strains and reduced fertility and increased mortality of infected hosts. It also assumes that one parasite strain is exclusively vertically...

Stable hypothesis for mixed models with balanced cross-nesting

Dário Ferreira, João Tiago Mexia, Sandra Saraiva Ferreira (2005)

Discussiones Mathematicae Probability and Statistics

Stable hypothesis are hypothesis that may refer either for the fixed part or for the random part of the model. We will consider such hypothesis for models with balanced cross-nesting. Generalized F tests will be derived. It will be shown how to use Monte-Carlo methods to evaluate p-values for those tests.

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