# 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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