Simulating differential equation models in R

Pre-conference tutorial at the useR!2014 conference, UCLA, Los Angeles, June 30 - July 3 2014

Karline Soetaert, Royal Netherlands Institute for Sea Research, NIOZ, The Netherlands.
Thomas Petzoldt, Dresden University of Technology, Faculty of Environmental Sciences, Germany.

Description

Differential equations can be used to describe exchanges of matter, energy, information or any other quantities as they vary in time and/or space.

We invite you to experience how nicely and flexibly R can be used to explore time-dependend behavior of dynamical systems, that occur in any field of science: mathematics, natural and life sciences, economics, finance and engineering.

Details

We will give an overview over the different solver functions available in packages deSolve and rootSolve. Practical examples will show that even numerically challenging systems can be efficiently solved in R and how external data can be handled. An outlook will demonstrate how partial differential equations (PDE) for reaction diffusion systems in 1D, 2D or 3D can be handled in R and how impressive computation performance can be approached.

• How to specify a model: Differential equation modelling made easy.
• Don't be afraid of stiffness: An overview over the solver functions.
• Dynamics, chaos and equilibria: Plotting, scenario comparison and root finding.
• Confronting models with data: Model fitting with package FME.
• Under control: Forcing functions and events.
• Diffusion, advection and reaction: Partial differential equations (PDE) with ReacTran.
• R without handbrake: Using matrices and compiled code.

Required Software

• the most recent version of R (>= 3.1.0)
• packages deSolve, rootSolve and FME
• Optional: R development tools
• Windows: RTools
• Linux: r-base-dev -- Installation on Ubuntu

Downloads and Preparatory Material

• Slides for the tutorial: pdf
• Guided web exercise: Solvers for Stiff Systems
• Guided web exercise: Fit a pharmacological model with package FME
• Guided web exercise: Compiled version of the Lorenz system
• More examples

The guided web exercises are made with InkScape and work best with Mozilla or Chrome.

Pre-conference discussion is possible on the mailig list: r-sig-dynamic-models@r-project.org

See also

useR!2014 conference -- deSolve project page

Interactive web applications of deSolve models at rforscience.com using the shiny package --- COOL!

Examples