Roots and steady-states

Description

Functions that:

(1) generate gradient and Jacobian matrices (full and banded),

(2) find roots of non-linear equations by the Newton-Raphson method,

(3) estimate steady-state conditions of a system of (differential) equations in full, banded or sparse form, using the Newton-Raphson method or by a dynamic run,

(4) solve the steady-state conditions for uni-and multicomponent 1-D, 2-D and 3-D partial differential equations, that have been converted to ODEs by numerical differencing (using the method-of-lines approach).

Details

Package: rootSolve
Type: Package
Version: 1.7
Date: 2010-10-10
License: GNU Public License 2 or above

rootSolve was created to solve the examples from chapter 7 (stability and steady-state) from the book of Soetaert and Herman, 2009.

Please cite this work when using rootSolve.

Author(s)

Karline Soetaert

References

Soetaert, K and Herman, PMJ, 2009. A Practical Guide to Ecological Modelling. Using R as a Simulation Platform. Springer, 372pp, ISBN 978-1-4020-8623-6.

Soetaert K., 2009. rootSolve: Nonlinear root finding, equilibrium and steady-state analysis of ordinary differential equations. R-package version 1.6

See Also

uniroot.all, to solve for all roots of one (nonlinear) equation

multiroot, to solve n roots of n (nonlinear) equations

steady, for a general interface to most of the steady-state solvers

steady.band, to find the steady-state of ODE models with a banded Jacobian

steady.1D, steady.2D, steady.3D, steady-state solvers for 1-D, 2-D and 3-D partial differential equations.

stode, iterative steady-state solver for ODEs with full or banded Jacobian.

stodes, iterative steady-state solver for ODEs with arbitrary sparse Jacobian.

runsteady, steady-state solver by dynamically running to steady-state

jacobian.full, jacobian.band, estimates the Jacobian matrix assuming a full or banded structure.

gradient, hessian, estimates the gradient matrix or the Hessian.

plot.steady1D, ... for plotting steady-state solutions.

package vignette rootSolve

Examples

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## Not run: 

## run demos
demo("Jacobandroots")
demo("Steadystate")

## open the directory with documents
browseURL(paste(system.file(package="rootSolve"), "/doc", sep=""))

## main package vignette
vignette("rootSolve")

## End(Not run)