deSolve (version 1.5-1)

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

Description

Functions that solve initial value problems of a system of first-order ordinary differential equations (ODE), of partial differential equations (PDE) and of differential algebraic equations (DAE).

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.

Details

ll{ Package: deSolve Type: Package Version: 1.5-1 Date: 2009-10-23 License: GNU Public License 2 or above }

The system of ODE's is written as an Rfunction or be 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

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

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

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

rk, rk4, euler for Runge-Kutta solvers.

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

Examples

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

## run demos
demo("rk_solvers") # comparison of lsoda with Runge-Kutta-Type Solvers
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 = ""))