## Tutorial: Simulating Differential Equation Models in R

Karline Soetaert, Netherlands Institute for Ecology, Netherlands.
Thomas Petzoldt, Dresden University of Technology, Germany.

### Abstract

R has become the most widely used systems for statistical data analysis, but it is also well suited for other disciplines in scientific computing. One of the fields where considerable progress has been made is the solution of differential equations. Package deSolve provides the useR with state-of-the-art technology for handling differential equations in R. The tutorial will concentrate on solving initial value problems of ordinary differential equations (ODE). 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.

### Outline

• 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.
• Under control: Forcing functions and events.
• Diffusion, advection and reaction: Partial differential equations (PDE) with ReacTran.
• R without handbrake: Using matrices and compiled code.

### Prerequisites

It will be assumed that participants have good knowledge of the R language and are familiar with ordinary differential equation models in any discipline. At least basic knowledge about numerical simulation methods would be helpful.

Preparatory material can be found on the deSolve web page.

### Intended Audience

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 people with background in natural, environmental and life sciences, as well as systems sciences, engineering, economics or any other discipline to experience how nicely and flexibly R can be used to explore time-dependend behavior of their dynamical systems.

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

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