Modeling with ODEs in Matlab – Part 3

Well, I feel like I should apologize for such a long delay between posts. It’s been a crazy summer that has included some vacation time plus an overseas trip to a conference. Regardless, I’m finally back in the swing of things and ready to write up Part 3! To recap: Lesson 1 and Lesson 2 looked at how ODEs are solved numerically and how higher order solutions are more accurate than naive implementations. Today we’ll look at two simulations of living systems (Lotka-Volterra and SIR). Finally, the series will conclude with a post on model fitting and a post about chaotic systems.
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Modeling with ODEs in Matlab – Part 2

Hello again! Today I’m back with Lesson 2 of our ongoing five part series on ODE modeling. Previously, Lesson 1 introduced the use of ODEs as a method of modeling population dynamics and discussed a simple method of evaluating the equations. Today, we will look at Matlab’s implementation of the Runge-Kutta method for solving ODEs. Lesson 3 will explore techniques for designing more realistic models. Lesson 4 will discuss methods for matching these abstract models to empirical data. Finally, we will play around with some fun ‘chaotic’ systems in Lesson 5.
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Modeling with ODEs in Matlab – Part 1

Hi everyone!  Today I am posting the first of a planned five part series on using Matlab to simulate systems of ordinary differential equations (ODEs).  This lesson will explore the meaning of a differential equation and look at a few possible ways to solve it.  Lesson Two will look at better ways to evaluate ODEs. Lesson Three will discuss designing and simulating models using systems of ODEs.  Lesson Four will explore ways to fit these models to empirical data.  Finally, we will examine some fun nonlinear ODEs and discuss ways to deal with their complexity in Lesson Five.
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