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Downloads
Views
Date
Relevance
Potential Scenario
92
views
50
downloads
0
comments
2014-Niemann-Miklos-Simple Method for Estimation of Parameters in First Order Systems
A simple method for estimation of parameters in first order systems with time delays is presented in this paper.
delay
time dely
step response
Modeling Scenario
222
views
154
downloads
0
comments
1-095-RatingChessPlayers-ModelingScenarios
The goal of this activity is to have students build a mathematical model involving a system of first order difference equations from a verbal description of a scenario.
simulation
chess
Elo's method
chess rating
Potential Scenario
180
views
29
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
92
views
43
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
Technique Narrative
325
views
162
downloads
0
comments
1-003-IntroNumericalMethods-TechniqueNarrative
We develop elementary approaches to numerically solving first order differential equations with Euler's Method, Improved Euler's Method and develop these geometrically to compute numeric solutions and compare them to analytic solutions.
analytic solution
Euler's method
improved Euler's method
Potential Scenario
141
views
60
downloads
0
comments
2015-Zhang-EtAl-On the Selection of ODE Models with Application to Predator-Prey Dynamical Models
We propose a computationally inexpensive approach that employs statistical estimation of the full model, followed by a combination of a least squares approximation (LSA) and the adaptive Lasso.
least-squares approximation
Spline modeling
Monte Carlo simulations
variable selection
adaptive LASSO
Modeling Scenario
247
views
524
downloads
0
comments
6-024-DronePackageDelivery-ModelingScenario
Students will derive a system of first order differential equations which describe the flight path of a drone delivering a package.
Vectors
Trigonometry
Flight
drones
parametric curve
Improved Euler Method
Runge-Kutta
Potential Scenario
129
views
54
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
210
views
62
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
108
views
36
downloads
0
comments
2007-Ramsay-Hooker-Campbell-Cao-Parameter estimation for differential equations-a generalized smoothing approach
We propose a new method for estimating parameters in models that are defined by a system of non-linear differential equations.
estimating equation
functional data analysis
Gauss–Newton method
parameter cascade
profiled estimation
dynamic system
Modeling Scenario
283
views
188
downloads
0
comments
3-011-EulerBallThrowing-ModelingScenario
If a tennis ball is thrown through the air it will hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the...
coding
dragon
Vectors
Euler's method
ball
Potential Scenario
118
views
55
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
153
views
63
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
366
views
230
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
112
views
72
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
194
views
306
downloads
0
comments
3-050-CometOrbitalMechanics-ModelingScenario
The broad goal of this activity is to use a basic numerical method to approximate the solution of an initial value problem. In this particular case, we will use Euler's method to help model the trajectory of a comet as it orbits the sun.
trajectory
Space
Euler's method
orbital mechanics
comet
orbit
Modeling Scenario
274
views
248
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
228
views
77
downloads
0
comments
2018-Joseph-EtAl-A Nonlinear differential equation model of Asthma effect of environmental pollution using LHAM
In this paper, we investigated a nonlinear differential equation mathematical model to study the spread of asthma in the environmental pollutants from industry and mainly from tobacco smoke from smokers in different type of population.
asthma
tobacco smoke
Liao’s Homotopy analysis Method (
environmental pollutants
Potential Scenario
172
views
68
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
149
views
47
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
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