R Package deSolve

Solvers for Initial Value Problems of Differential Equations (ODE, DAE, DDE)

Overview

deSolve is a comprehensive R package for solving initial value problems of differential equations. It provides robust numerical solvers for:

• Ordinary Differential Equations (ODE)
• Differential Algebraic Equations (DAE)
• Partial Differential Equations (PDE) using the method of lines
• Delay Differential Equations (DDE)

The package can be used in scientific computing, ecological modeling, pharmacokinetics, and many other fields requiring numerical integration of dynamic systems.

Features

• Multiple solver algorithms (lsoda, lsode, lsodes, vode, ode45, rk4, euler, ...)
• Support for compiled code (C, Fortran) for improved performance
• Forcing functions, event handling, and plotting

Installation

Stable version from CRAN (recommended)

install.packages("deSolve")

Development version from Github (unstable)

# install.packages("remotes")
remotes::install_github("tpetzoldt/deSolve")

Quick Example

library(deSolve)

## Chaos in the Atmosphere
Lorenz <- function(t, state, parameters) {
  with(as.list(c(state, parameters)), {
    dX <-  a * X + Y * Z
    dY <-  b * (Y - Z)
    dZ <- -X * Y + c * Y - Z
    list(c(dX, dY, dZ))
  })
}

parameters <- c(a = -8/3, b = -10, c = 28)
state      <- c(X = 1, Y = 1, Z = 1)
times      <- seq(0, 100, by = 0.01)

out <- ode(y = state, times = times, func = Lorenz, parms = parameters)

plot(out)

License

deSolve is Free and Open Source Software, released under the GPL 2.0 or GPL 3.0 license.

Documentation

For comprehensive documentation and tutorials, visit:

• Package website: https://cran.r-project.org/package=deSolve
• Example models collection: https://github.com/tpetzoldt/dynamic-R-models
• and more

Citation

If you use deSolve in your research, please cite:

Soetaert, K., Petzoldt, T., and Setzer, R. W. (2010). Solving Differential Equations in R: Package deSolve. Journal of Statistical Software, 33(9), 1-25. https://doi.org/10.18637/jss.v033.i09

Contributing

This is the active development repository for deSolve. Previous development occured on R-Forge at http://desolve.r-forge.r-project.org/

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Thomas & Karline 2026-02-04