deSolve - Differential Equations in R

'deSolve' is an add-on package for the open source data analysis system R for the numerical treatment of systems of differential equations

What is in deSolve?

deSolve contains functions that solve initial value problems of a system of first-order ordinary differential equations (ODE), of partial differential equations (PDE), of differential algebraic equations (DAE), and of delay differential equations (DDE). The functions provide an interface to the FORTRAN functions lsoda, lsodar, lsode, lsodes of the ODEPACK collection, to the FORTRAN functions dvode, zvode, daspk and radau5, and a C-implementation of solvers of the Runge-Kutta family with fixed or variable time steps.

The package contains also routines designed for solving ODEs resulting from 1-D, 2-D and 3-D partial differential equations (PDE) that have been converted to ODEs by numerical differencing.

Project web pages

• The package at CRAN
• The project summary page at R-Forge.

Documentation

Manual and Tutorials

• The Reference Manual at CRAN
• Tutorial: Solving Initial Value Differential Equations in R
• Tutorial: deSolve: Writing Code in Compiled Languages
• Simulating Differential Equation Models in R. Tutorial held at the useR!2011 conference at the University of Warwick. [slides with embedded examples]

Papers

• Soetaert, K. and Petzoldt, T. (2011): Solving ODEs, DAEs, DDEs and PDEs in R. Journal of Numerical Analysis, Industrial and Applied Mathematics (JNAIAM) 6(1-2), 51-65. http://jnaiam.org/uploads/jnaiam_6_4.pdf
• Soetaert, K., Petzoldt, T. & Setzer, R. W. (2010): Solving differential equations in R: package deSolve. Journal of Statistical Software 33(9), 1-25. http://www.jstatsoft.org/v33/i09
• Soetaert, K. & Petzoldt, T. (2010): Inverse modelling, sensitivity and Monte Carlo analysis in R using package FME. Journal of Statistical Software 33(3), 1-28. http://www.jstatsoft.org/v33/i03
• Soetaert, K., Meysman, F. and Petzoldt, T. (2010) Solving Differential Equations in R. AIP Conf. Proc. Volume 1281, pp. 31-34 ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010; doi:10.1063/1.3498463
• Soetaert, K. Petzoldt, T. & Setzer, R. W. (2010): Solving differential equations in R. The R Journal 2(2), 5-15. http://journal.r-project.org/

Books that make use of deSolve

The following books make extensive use of deSolve:

• Soetaert, Karline, Cash, Jeff and Mazzia, Francesca (2012) Solving Differential Equations in R. Springer, 248 pp. [book homepage]
• Soetaert, Karline and Herman, Peter M.J. (2009) A Practical Guide to Ecological Modelling Using R as a Simulation Platform. Springer, 372 pp. [book homepage]
• Stevens, M. Henry H. (2009) A Primer of Ecology with R. Springer. 388 pp. [book homepage]

The lab manual of the following book uses the predecessor package "odesolve". It works also with "deSolve":

• Stephen P. Ellner & John Guckenheimer (2006). Dynamic Models in Biology. Princeton University Press. [book homepage], [supplemental material with R lab manual]

Conference Talks

• Petzoldt T., Dynamic simulation models - is R powerful enough? UseR!2009, July 8-10, Rennes, France [slides]
• Soetaert K., Mathematical modelling of the environment - are there enough data? UseR!2009, July 8-10, Rennes, France [slides]
• Soetaert, K., Meysman, F. and Petzoldt, T. (2010) Solving Differential Equations in R. ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics, September 19-25, Rhodos, Greece. 2010; doi:10.1063/1.3498463
• Petzoldt, T. and Soetaert, K. (2011) Using R for Systems Understanding - A Dynamic Approach. UseR!2011, August 16-18, University of Warwick, Coventry, UK [slides]

Developers

• Karline Soetaert, Royal Netherlands Institute for Sea Research (NIOZ)
• Thomas Petzoldt, Technische Universität Dresden
• Woodrow Setzer, US Environmental Protection Agency (EPA)

Related Packages

• rootSolve: Nonlinear root finding, equilibrium and steady-state analysis of ordinary differential equations.
• bvpSolve: Functions that solve boundary value problems (BVP) of systems of ordinary differential equations.
• ReacTran: Routines for developing models that describe reaction and advective-diffusive transport in one, two or three dimensions.
• marelac: Tools, constants and conversions for marine and lacustrine sciences.
• simecol: An object oriented framework for structured implementation of dynamic models.
• FME: Flexible Modelling Environment: sensitivity analysis, parameter fitting and MCMC.

Mailing list

Discussions about deSolve should be directed to the mailing list: r-sig-dynamic-models@r-project.org

This Special Interest Group for Dynamic Simulation Models in R is a forum for discussing the use of R for implementation, simulation and analysis of dynamic simulation models. The list covers differential equation models as well as other dynamic systems in different application areas: natural sciences, engineering, economy and many others.

Date: 2013-04-07