CRAN Task View: Differential Equations

Maintainer:Karline Soetaert, Thomas Petzoldt
Contact:karline.soetaert at

Differential equations (DE) are mathematical equations that describe how a quantity changes as a function of one or several (independent) variables, often time or space. Differential equations play an important role in biology, chemistry, physics, engineering, economy and other disciplines.

Differential equations can be separated into stochastic versus deterministic DEs. Problems can be split into initial value problems versus boundary value problems. One also distinguishes ordinary differential equations from partial differential equations, differential algebraic equations and delay differential equations. All these types of DEs can be solved in R. DE problems can be classified to be either stiff or nonstiff; the former type of problems are much more difficult to solve.

The dynamic models SIG is a suitable mailing list for discussing the use of R for solving differential equation and other dynamic models such as individual-based or agent-based models.

This task view was created to provide an overview on the topic. If we forgot something, or if a new package should be mentioned here, please let us know.

Stochastic Differential Equations (SDEs)

In a stochastic differential equation, the unknown quantity is a stochastic process.

Ordinary Differential Equations (ODEs)

In an ODE, the unknown quantity is a function of a single independent variable. Several packages offer to solve ODEs.

Delay Differential Equations (DDEs)

In a DDE, the derivative at a certain time is a function of the variable value at a previous time.

Partial Differential Equations (PDEs)

PDEs are differential equations in which the unknown quantity is a function of multiple independent variables. A common classification is into elliptic (time-independent), hyperbolic (time-dependent and wavelike), and parabolic (time-dependent and diffusive) equations. One way to solve them is to rewrite the PDEs as a set of coupled ODEs, and then use an efficient solver. Note that, to date, PDEs in R can only be solved using finite differences. At some point, we hope that finite element and spectral methods will become available.

Differential Algebraic Equations (DAEs)

Differential algebraic equations comprise both differential and algebraic terms. An important feature of a DAE is its differentiation index; the higher this index, the more difficult to solve the DAE.

Boundary Value Problems (BVPs)

BVPs have solutions and/or derivative conditions specified at the boundaries of the independent variable.

Population ODE modeling


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