Solving Differential Equations in R

CONTRIBUTEDRESEARCHARTICLES5 Solving Differential Equations in Rby Karline Soetaert, Thomas Petzoldt and R. WoodrowSetzer1 AbstractAlthough R is still predominantly ap-plied for statistical analysis and graphical repre-sentation, it is rapidly becoming more suitablefor mathematical computing. One of the fieldswhere considerable progress has been made re-cently is the solution of Differential we give a brief overview of differentialequations that can now be solved by Equations describe exchanges of matter,energy, information or any other quantities, often asthey vary in time and/or space. Their thorough ana-lytical treatment forms the basis of fundamental the-ories in mathematics and physics, and they are in-creasingly applied in chemistry, life sciences and Equations are solved by integration,but unfortunately, for many practical applicationsin science and engineering, systems of differentialequations cannot be integrated to give an analyticalsolution, but rather need to be solved advanced numerical algorithms that solvedifferential Equations are available as (open-source)

With the introduction of R-package odesolve (Setzer,2001), it became possible to use R (R Devel-opment Core Team,2009) for solving very simple ini-tial value problems of systems of ordinary differen-tial equations, using the lsoda algorithm ofHind-marsh(1983) andPetzold(1983). However, many real-life applications, including physical transport

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