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)computer codes, written in programming languageslike FORTRAN or C and that are available fromrepositories like GAMS ( ) orNETLIB ( ).

Numerical solution of a system of differential equa-tions is an approximation and therefore prone to nu-merical errors, originating from several sources: 1.time step and accuracy order of the solver, 2.floating point arithmetics, 3.properties of the differential system and stabil-ity of the solution algorithm.

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  Into, Differential, Solving, Equations, Equa, Solving differential equations in r, Equa tions

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