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Downloads
Views
Date
Relevance
Technique Narrative
181
views
245
downloads
0
comments
1-060-RegularPerturbation-TechniqueNarrative
This paper presents an introduction to a set of analytical approximations referred to as regular perturbation. This is a particular mathematical tool within the broader set of perturbation methods.
perturbation
regular perturbation
asymptotic expansions
analytical approximation
Bernoulli equation
Potential Scenario
141
views
40
downloads
0
comments
2015-Sivakumar-EtAl-Approximate Analytical Expression of Concentrations in a Kinetic Model for Biogas Generation from Banana Waste
The initial value problem in a kinetic model for biogas generation from banana waste is discussed. The model involves the system of non-linear differential equations which has variety of non-linear rate function.
chemical kinetics
Michaelis-Menten kinetics
anaerobic digestion
acidogenic steps
banana
methanogenic steps
wastes
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
Technique Narrative
374
views
120
downloads
0
comments
2-005-LinearizeItAll-TechniqueNarrative
Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form solutions may be obtained.
computation
error
Torricelli's Law
data fitting
linear approximation
Potential Scenario
97
views
44
downloads
0
comments
1987-Claude-Marmasse-Studies on differential equations of enzyme kinetics-Biomolecular scheme
The integral curve is compared with the solutions given by the two classical approximations to the problem: it is shown that the steady-state approximation is to be preferred to the rapid equilibrium theory as a general method.
steady-state model
isoclines
enzyme kinetics
Technique Narrative
352
views
146
downloads
0
comments
2-001-NumericalMethodsComparisons-TechniqueNarrative
This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and compare their CPU times.
Euler's method
improved Euler's method
RK3 methods
RK4 methods
order of accuracy
absolute error
CPU time
Potential Scenario
132
views
38
downloads
0
comments
1999-Marchand-McDevitt-Learning Differential Equations by Exploring Earthquake Induced Structural Vibrations
The project takes full advantage of analytical, numerical, and qualitative techniques to explore the mechanical vibrations of buildings during an earthquake.
earthquake
nondimensionalization
Coulomb damping
mechanical vibration
Potential Scenario
333
views
48
downloads
0
comments
2018-Hu-Huang-Dynamic Regulation Responding to an External Stimulus
This study examines the dynamic regulation process responding to an external stimulus. This study introduces the driven damped oscillator model which has an additional parameter to identify different patterns of the steady state.
dynamical systems
regulation
steady state
sales model
external stimulus
Potential Scenario
348
views
68
downloads
0
comments
2017-Varanis-Mereles-Mathematical Model of a Vehicle Crash A Case Study
The model proposed in this paper allows one to obtain the parameters of the system, and then compare them with the ones obtained experimentally to test the suitability of the model with the vehicle crash.
case study
Runge-Kutta
spring mass damper
vehicle crash
Modeling Scenario
321
views
220
downloads
0
comments
1-102C-CancerGrowth-ModelingScenario
This module guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including exponential, power law, Bertalanffy, logistic, and...
optimization
cancer
logistic
exponential
prediction
tumor
growth
data fitting
power law
Bertanffy
Gompertz
Modeling Scenario
196
views
84
downloads
0
comments
3-085-SimplePendulum-ModelingScenario
Thestudent is asked to derive and solve a differential equation that gives the position (angle
Newton's Second Law of Motion
pendulum
kinetic energy
potential energy
Conservation of Energyt
initial conditions
small angle approximation
Taylor polynomial
percent error
Modeling Scenario
193
views
378
downloads
0
comments
9-020-HeatDiffusion-ModelingScenario
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario.
laboratory
Diffusion
heat
Modeling Scenario
183
views
167
downloads
0
comments
3-069-HeatInBar-ModelingScenario
The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches.
heat transfer
experiment
conduction
convection
boundary conditions
finite volume method
Modeling Scenario
174
views
181
downloads
0
comments
3-064-GearTrain-ModelingScenario
Students model an input-output mechanical system of gears with a second order, non-homogeneous, ordinary differential equation with constant coefficients. The model incorporates friction and moments of inertia of the gear train components.
friction
gear
spur gear
gear train
torque
gear ratio
angular acceleration
angular velocity
moment of inertia
double reduction gear
Modeling Scenario
212
views
327
downloads
0
comments
3-090-OneSpringMass-ModelingScenario
We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their model to approximate the value of the spring...
undamped
sum of square errors
mass spring
Hooke's Law
oscilation
least-squares approximation
Potential Scenario
153
views
38
downloads
0
comments
2009-Chellaboina-EtAl-Modeling And Analysis-Mass Action Kinetics
Mass-action kinetics are used in chemistry and chemical engineering to describe the dynamics of systems of reactions, that is, reaction networks. These models are a special form of compartmental systems, involving mass- and energy-balance relations.
dynamical systems
chemical reaction
reaction network
mass action
Potential Scenario
183
views
42
downloads
0
comments
1999-Khorasheh-Ahmadi-Gerayeli-Application of Direct Search Optimization for Pharmacokinetic Parameter Estimation
For simple pharmacokinetic compartmental models, analytical solution to the governing differential equations provide a mean to evaluate the associated rate constants. Such methods, however, can not be used used for more complex multi-compartment...
sum of square errors
least squares
pharmacokinetics
lineteics
compartmental models
direct search
Potential Scenario
259
views
41
downloads
0
comments
2018-Robert_Phair-Differential_equation_methods_for_simulation_of_GFP_kinetics_in_non–steady_state_experiments
Here, we derive new tracer kinetic analytical methods for non–steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological processes.
protein quality control
kinetics
Cells
steady state
chemical kinetics
fluouresence
photoactivation
inytracellular
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
116
views
35
downloads
0
comments
2012-Yuan_Yuan-A coupled plankton system with instantaneous and delayed predation
We present two simple plankton population models: one has instantaneous predation, another has delayed predation.
phytoplankton
bifurcation
orbits
herbivorous zooplankton
effect of fish
maturation time delay
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