deSolve (version 1.8.1)

deSolve-package: General Solvers for Initial Value Problems of Ordinary Differential Equations (ODE), Partial Differential Equations (PDE), Differential Algebraic Equations (DAE) and delay differential equations (DDE).

Description

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 delay differential equations.

The functions provide an interface to the FORTRAN functions lsoda, lsodar, lsode, lsodes of the ODEPACK collection, to the FORTRAN functions dvode and daspk and a C-implementation of solvers of the Runge-Kutta family with fixed or variable time steps.

The package contains 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. It includes root-finding (or event location) and provides access to lagged variables and derivatives.

Details

ll{ Package: deSolve Type: Package Version: 1.8 Date: 2010-09-01 License: GNU Public License 2 or above }

The system of differential equations is written as an Rfunction or defined in compiled code that has been dynamically loaded, see package vignette (vignette(compiledCode)) for details. The solvers may be used as part of a modeling package for differential equations, or for parameter estimation using any appropriate modeling tool for non-linear models in Rsuch as optim, nls, nlm or nlme.

References

Karline Soetaert, Thomas Petzoldt, R. Woodrow Setzer (2010). Solving Differential Equations in R: Package deSolve Journal of Statistical Software, 33(9), 1--25. http://www.jstatsoft.org/v33/i09/

Alan C. Hindmarsh, 1983. ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), North-Holland, Amsterdam, pp. 55-64.

L. R. Petzold, 1983. A Description of DASSL: A Differential/Algebraic System Solver, in Scientific Computing, R. S. Stepleman et al. (Eds.), North-Holland, Amsterdam, pp. 65-68.

P. N. Brown, G. D. Byrne, and A. C. Hindmarsh, 1989. VODE: A Variable Coefficient ODE Solver, SIAM J. Sci. Stat. Comput., 10, pp. 1038-1051.

See also the references given on the specific help pages of the different methods.

See Also

ode for a general interface to most of the ODE solvers, ode.band for solving models with a banded Jacobian,

ode.1D, ode.2D, ode.3D, for integrating 1-D, 2-D and 3-D models, dede for a general interface to the delay differential equation solvers,

lsoda, lsode, lsodes, lsodar, vode, for ODE solvers of the Livermore family,

daspk, for a DAE solver up to index 1, of the Livermore family,

radau for integrating DAEs up to index 3 using an implicit Runge-Kutta,

rk, rkMethod, rk4, euler for Runge-Kutta solvers,

DLLfunc, DLLres, for testing model implementations in compiled code,

forcings, events, for how to implement forcing functions (external variables) and events (sudden changes in state variables), lagvalue, lagderiv, for how to get access to lagged values of state variables and derivatives.

Examples

## show examples (see respective help pages for details)
example(aquaphy)
example(lsoda)
example(ode.band)
example(ode.1D)
example(ode.2D)
example(ode.3D)
example(dede)

## run demos
demo("odedim")     # partial differential equations
demo("CCL4model")  # a model fitting example (this will take some time)

## open the directory with source code of demos
browseURL(paste(system.file(package = "deSolve"), "/demo", sep = ""))

## open the directory with R sourcecode examples
browseURL(paste(system.file(package = "deSolve"), "/doc/examples", sep = ""))
## open the directory with C and FORTRAN sourcecode examples
browseURL(paste(system.file(package = "deSolve"), "/doc/examples/dynload", sep = ""))

## show package vignette with how to use deSolve
## + source code of the vignette
vignette("deSolve")
edit(vignette("deSolve"))

## show package vignette with tutorial about how to use compiled models
## + source code of the vignette
## + directory with C and FORTRAN sources
vignette("compiledCode")
edit(vignette("compiledCode"))
browseURL(paste(system.file(package = "deSolve"), "/doc", sep = ""))