
5010SMatrixExponential
12 Sep 2019   Contributor(s):: Kurt Bryan
The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and exercises. It also includes an introduction to...

2017Bonin EtAl  Math Modeling Based on ODE for Vaccinology
09 Dec 2018   Contributor(s):: Brian Winkel
Bonin, C.R.B. Et al. 2017. Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology. Human Vaccines and Immunotherapy. 13(2): 484–489.Abtract: New contributions that aim to accelerate the development or to improve the efficacy and safety of...

2001TextSNumericalMethodsComparisons
18 Aug 2018   Contributor(s):: Swarn Singh
It is not always possible to solve a differential equation analytically.This material makes an effort to teach the basics of numerical methods for first order differential equations by following graphical and numerical approaches. Here we also discuss the order of accuracy of the methods and...

6018SExploringSIRModel
30 May 2018   Contributor(s):: Stanley Florkowski, Ryan Miller
Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

2016CamporesiImpulsive response method using factorization.
03 Mar 2018   Contributor(s):: Roberto Camporesi
Camporesi, Roberto. 2016. A fresh look at linear ordinary differential equations with constant coefficients. Revisiting theimpulsive response method using factorization. Int. J. Math. Educ. Sci. Technol. 47(1): 8299Summary: We present an approach to the impulsive response method for solving...

2003RasmussenKeynesLinesOfEigenVectorsSolutionsToSytemsOfLinearDifferentialEquations
03 Mar 2018   Contributor(s):: Chris Rasmussen, Michael Keynes
Rasmussen, Chris and Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations. PRIMUS. 13(4): 308320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...

2012NokkaewEtAlEstimation Of Algae Growth Mode lParameters Using Genetic Algorithm
08 Sep 2017   Contributor(s):: Brian Winkel
Nokkaew, A. Et Al. Estimation of Algae Growth Model Parameters by a Double Layer Genetic Algorithm. WSEAS TRANSACTIONS on COMPUTERS. 11(11): 377386. http://www.wseas.org/multimedia/journals/computers/2012/56122.pdf . Accessed 7 September 2017.ABSTRACT: This paper presents a double layer...

A Particular Solutions Formula For Inhomogeneous Arbitrary Order Linear Ordinary Differential Equations
24 May 2017   Contributor(s):: CLAUDE MICHAEL CASSANO
A particular solution for any nonhomogeneous linear second, third, and fourth order ordinary differential equation is generally determined. Applying what was determined thus; and following by example a particular solution formula for arbitrary order is obtained. Finding a particular solutions to...

On the General Solution of Initial Value Problems of Ordinary Differential Equations Using the Method of Iterated Integrals
10 Jan 2017   Contributor(s):: Ahsan Amin
Our goal is to give a very simple, effective and intuitive algorithm for the solution of initial value problem of ordinary differential equations of first order and higher order with constant, variable or nonlinear coefficients and systems of these ordinary differential equations. We find...

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2011Zhao Systems Biology  Differential Equations  Survey
24 Jun 2015   Contributor(s):: D. I. Zhao
Zhao, D. I. 2011. Differential Equation Models for Systems Biology: A Survey. Computational Analysis and Modeling, Lousiana Tech University, Ruston LA USA. 30 pp. http://www.advancedcomputing.cn/sys_bio_review.pdf . Accessed 22 June 2015.Abstract: In this paper, we will...