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Downloads
Views
Date
Relevance
Potential Scenario
199
views
40
downloads
0
comments
2012-Campbell-EtAl-Parameter estimation in differential equation models with constrained states
We introduce a method to estimate parameters and states from a differential equation model while enforcing interpretability constraints such as monotone or non‐negative states.
chemical engineering
smoothing-based relaxation method
Potential Scenario
106
views
54
downloads
0
comments
2003-Givens-Bonfima-Direct observation of normal modes in coupled oscillators
We propose a simple and inexpensive method to directly observe each normal mode of a system of coupled oscillators, as well as to measure its corresponding frequency, without performing Fourier analysis or using expensive apparatus.
frequency
resonance
coupled oscillator
Potential Scenario
142
views
55
downloads
0
comments
2018-Adeniji-EtAl-InverseProblemHolling-TannerModel
We consider the inverse problem of parameter identification of nonlinear system of ODEs for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval.
goal function
absolute error curves
invers method
holling-Tanner model
Potential Scenario
236
views
82
downloads
0
comments
2017-Justin_Krueger-Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology
We demonstrate the feasibility of principal differential analysis using simulation studies and then apply the method to intestinal and vaginal microbiota data.
microbiology
Lotka Volterrra
microbiota
Potential Scenario
137
views
70
downloads
0
comments
2016-Roberto_Camporesi-A fresh look at linear ordinary differential equations with constant coefficients
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator.
impulse
Green functions
instructional exposition
Potential Scenario
193
views
81
downloads
0
comments
2009-Peter-Howard-Modeling With ODE
This is a set of class notes rich in examples and ideas for modeling. There is some MatLab code in support of some of the activities.
rates
competition
population
epidemic
pendulum
carbon dating
reaction chemistry
mechanics
planetary motion
drag racing
Hamilton’s method
variational method
Modeling Scenario
399
views
266
downloads
0
comments
1-024-MalariaControl-ModelingScenario
This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and non-linear (logistic growth) differential equations.
population dynamics
malaria
Policy
Decision-making
Euler's method
pharmacokinetics
mosquito
improved Euler's method
Huen's method
US Army
Potential Scenario
132
views
79
downloads
0
comments
2014-Wang-EtAl-Estimating Mixed-Effects Differential Equation Models
When multiple replicates of measurements are available for the dynamic process, it is of great interest to estimate mixed-effects in the ODE model for the process. We propose a semiparametric method to estimate mixed-effects ODE models.
pharmacokinetics
dynamic models
smoothing
spline
mixed-effects models
HiV combination therapy
Modeling Scenario
311
views
299
downloads
0
comments
6-002-EulerCromerPendulum-ModelingScenario
This activity introduces students to the concept of numerical stability. While modeling a simple pendulum, students compare performance of the semi-implicit Euler-Cromer method with Euler's method and the higher-order Improved Euleror algorithm.
pendulum
semi-implicit methods
Euler-Cromer
numerical solvers
Potential Scenario
189
views
80
downloads
0
comments
2017-Jean-Roux-Mathematical Models in Air Quality Problems
Presents many models with analysis in air quality control. Starts with chemical kinetics models and builds complexity to PDE models.
air pollution effects on forest ecosystems
finite volume method
boundary layer
chemical kinetics
finite difference
emissions
depositions
advection
Potential Scenario
167
views
55
downloads
0
comments
2016-Wilkie-EtAl-Using ODEs to Explore Cancer-Immune Dynamics and Tumor Dormancy
Here we present a general method using ordinary differential equations (ODEs) to model and analyze cancer-immune interactions, and in particular, immune-induced tumor dormancy.
cancer
tumor-inhibiting cytotoxic action
tumor-promoting inflammation
immune-induced tumor dormancy
tumor growth dynamics
Technique Narrative
521
views
229
downloads
0
comments
1-002-IntegratingFactor-TechniqueNarrative
We develop a strategy to solve first order differential equations by transforming one side of the equation to the derivative of a product of two functions, thereby making it easy to antidifferentiate that side.
Integrating Factor
Potential Scenario
812
views
52
downloads
0
comments
2019-Stender_EtAl-Recovery_Of_Differential_Equations_From_Impulse_Response
In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation.
time series
regression
response
impulse
oscillation
signal processing
sparse regression
system identification
Technique Narrative
598
views
240
downloads
0
comments
1-001-SepartionOfVariables-TechniqueNarrative
We discuss strategies to solve first order, ordinary differential equations with mathematical models when the variables may be separated.
solutions
strategy
method
applications
Modeling Scenario
396
views
494
downloads
0
comments
6-068-VisualizingPredator-PreyCycles
In this modeling scenario, we propose a gentle introduction to limit cycles using nullcline analysis and a spreadsheet graphical approach via the fourth-order Runge-Kutta method. We will be offering three predator-prey models, each more complex...
nullclines
predator-prey
Geometry
predator
Runge-Kutta
prey
limit cycle
Potential Scenario
146
views
70
downloads
0
comments
2011-Gaff-Lenhart-Use of optimal control models to predict treatment time for managing tick-borne disease
Tick-borne diseases have been on the rise recently, and correspondingly, there is an increased interest in implementing control measures to decrease the risk. Optimal control provides an ideal tool to identify the best method for reducing risk.
disease
optimal control
TICK
tick mode
ehrlichiosis
bang bang control
Potential Scenario
157
views
54
downloads
0
comments
2003-Rasmussen-Keynes-Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations
The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of eigenvectors and corresponding solutions to systems of two first order linear ordinary differential equations with constant...
instructional design
eigenvalues
eigenvalue analysis
Potential Scenario
131
views
47
downloads
0
comments
2003-Bohren-Dimensional analysis-falling bodies--fine art of not solving differential equations
Dimensional analysis is a simple, physically transparent and intuitive method for obtaining approximate solutions to physics problems, especially in mechanics.
falling body
dimensional analysis
drag
Potential Scenario
160
views
54
downloads
0
comments
2019-Hu-Treinen-One-step_method_for_modelling_longitudinal_data_with_differential_equations
This study proposes a new approach to estimate the parameters in differential equation models used to describe non-linear trajectories of longitudinal data.
simulation
parameter estimation
shopping
fitting
behaviour
Technique Narrative
516
views
591
downloads
0
comments
5-005-StiffDifferentialEquations-TechniqueNarrative
This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples. Stiffness is a property that a system of ODE's may posses that make it difficult to solve numerically.
Euler's method
explicit methods
implicit methods
stiff
sitffness
stiff differential equation
instability
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