We consider a coupled PDE–ODE model governing the bacterial dynamics of anaerobic biodegradation household waste in landfill. The biological activity, represented with non linear system ordinary differential equations (ODE), takes place an unsaturated porous medium by Darcy law. transform initial into fully PDE where distribution is spatialized as reaction–diffusion equations. carry out mathema...

A laminar, two dimensional, steady boundary layer Newtonian conducting fluid flow passes over a permeable shrinking sheet in the presence of a uniform magnetic field is investigated. The governing equations have converted to ordinary nonlinear differential equations (ODE) by using appropriate similarity transformations. The main idea is to transform ODE with infinite boundary condition into oth...

Models based on ordinary differential equations (ODE) are widespread tools for describing dynamical systems. In biomedical sciences, data from each subject can be sparse making difficult to precisely estimate individual parameters by standard non-linear regression but information can often be gained from between-subjects variability. This makes natural the use of mixed-effects models to estimat...

We present a new tool, GPA, that can generate key performance measures for very large systems. Based on solving systems of ordinary differential equations (ODEs), this method of performance analysis is far more scalable than stochastic simulation. The GPA tool is the first to produce higher moment analysis from differential equation approximation, which is essential, in many cases, to obtain an...

Some engineering systems are naturally described by differential-algebraic equations (DAE), whereas it may be difficult or impossible to model them with ordinary differential equations (ODE). This paper proposes an approach to fault diagnosis for systems described by DAEs. Through a particular discretization method and under realistic assumptions, the considered continuous time DAE model is tra...

This paper discusses the application of moment closures to continuous Markov chains derived from process algebras such as GPEPA and MASSPA. Two related approaches are being investigated. Firstly we re-formulate normal moment closure in a process algebra framework using Isserlis’ theorem. Secondly we apply a mixture of this normal closure and less precise moment closures for the purpose of reduc...

Modeling in biology is mainly grounded in mathematics, and specifically on ordinary differential equations (ODE). The programming language approach is a complementary and emergent tool to analyze the dynamics of biological networks. Here we focus on BlenX showing how it is possible to easily re-use ODE models within this framework. A budding yeast cell cycle example demonstrates the advantages ...

This paper presents an evolutionary method for identifying the gene regulatory network from the observed time series data of gene expression using a system of ordinary differential equations (ODEs) as a model of network. The structure of ODE is inferred by the Multi Expression Programming (MEP) and theODE’s parameters are optimized by using particle swarm optimization (PSO). The proposed method...

Ordinary differential equations (ODEs) provide a classical framework to model the dynamics of biological systems, given temporal experimental data. Qualitative analysis of the ODE model can lead to further biological insight and deeper understanding compared to traditional experiments alone. Simulation of the model under various perturbations can generate novel hypotheses and motivate the desig...

Differential Algebraic Equations (DAEs) are a general and implicit form of differential equations. DAEs are often used to represent physical systems such as dynamics of solids or chemical interactions. These equations are different from Ordinary Differential Equations (ODEs) in the sense that some of the dependent variables occur without their derivatives. Validated simulation of ODEs has recen...