ode.band {deSolve} | R Documentation

## Solver for Ordinary Differential Equations; Assumes a Banded Jacobian

### Description

Solves a system of ordinary differential equations.

Assumes a banded Jacobian matrix, but does not rearrange the state variables (in contrast to ode.1D). Suitable for 1-D models that include transport only between adjacent layers and that model only one species.

### Usage

    ode.band(y, times, func, parms, nspec = NULL, dimens = NULL,
      bandup = nspec, banddown = nspec, method = "lsode", names = NULL,
      ...)

### Arguments

`y` | the initial (state) values for the ODE system, a vector. If `y` has a name attribute, the names will be used to label the output matrix.
`times` | time sequence for which output is wanted; the first value of `times` must be the initial time.

`func`

either an R-function that computes the values of the derivatives in the ODE system (the model definition) at time `t`, or a character string giving the name of a compiled function in a dynamically loaded shared library.

If `func` is an R-function, it must be defined as: `func <- function(t, y, parms, ...)`. `t` is the current time point in the integration, `y` is the current estimate of the variables in the ODE system. If the initial values `y` has a `names` attribute, the names will be available inside `func`. `parms` is a vector or list of parameters; `...` (optional) are any other arguments passed to the function.

The return value of `func` should be a list, whose first element is a vector containing the derivatives of `y` with respect to `time`, and whose next elements are global values that are required at each point in `times`.The derivatives must be specified in the same order as the state variables `y`.

`parms` | parameters passed to `func`.
`nspec` | the number of *species* (components) in the model.
`dimens` | the number of boxes in the model. If `NULL`, then `nspec` should be specified.
`bandup` | the number of nonzero bands above the Jacobian diagonal.
`banddown` | the number of nonzero bands below the Jacobian diagonal.
`method` | the integrator to use, one of `"vode"`, `"lsode"`, `"lsoda"`, `"lsodar"`, `"radau"`.
`names` | the names of the components; used for plotting.
`...` | additional arguments passed to the integrator.

### Details

This is the method of choice for single-species 1-D reactive transport models.

For multi-species 1-D models, this method can only be used if the state variables are arranged per box, per species (e.g. A[1], B[1], A[2], B[2], A[3], B[3], ... for species A, B). By default, the model function will have the species arranged as A[1], A[2], A[3], ... B[1], B[2], B[3], ... in this case, use `ode.1D`.

See the selected integrator for the additional options.

### Value

A matrix of class `deSolve` with up to as many rows as elements in `times` and as many columns as elements in `y` plus the number of "global" values returned in the second element of the return from `func`, plus an additional column (the first) for the time value. There will be one row for each element in `times` unless the integrator returns with an unrecoverable error. If `y` has a names attribute, it will be used to label the columns of the output value.

The output will have the attributes `istate` and `rstate`, two vectors with several elements. See the help for the selected integrator for details. the first element of istate returns the conditions under which the last call to the integrator returned. Normal is `istate = 2`. If `verbose = TRUE`, the settings of `istate` and `rstate` will be written to the screen.

### Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

### See Also

- `ode` for a general interface to most of the ODE solvers,

- `ode.1D` for integrating 1-D models

- `ode.2D` for integrating 2-D models

- `ode.3D` for integrating 3-D models

- `lsode`, `lsoda`, `lsodar`, `vode` for the integration options.

`diagnostics` to print diagnostic messages.

### Examples

    ## =======================================================================
    ## The Aphid model from Soetaert and Herman, 2009.
    ## A practical guide to ecological modelling.
    ## Using R as a simulation platform. Springer.
    ## =======================================================================

    ## 1-D diffusion model

    ## ================
    ## Model equations
    ## ================
    Aphid <- function(t, APHIDS, parameters) {
      deltax  <- c (0.5*delx, rep(delx, numboxes-1), 0.5*delx)
      Flux    <- -D*diff(c(0, APHIDS, 0))/deltax
      dAPHIDS <- -diff(Flux)/delx + APHIDS*r

      list(dAPHIDS)   # the output
    }

    ## ==================
    ## Model application
    ## ==================

    ## the model parameters:
    D         <- 0.3    # m2/day  diffusion rate
    r         <- 0.01   # /day    net growth rate
    delx      <- 1      # m       thickness of boxes
    numboxes  <- 60

    ## distance of boxes on plant, m, 1 m intervals
    Distance  <- seq(from = 0.5, by = delx, length.out = numboxes)

    ## Initial conditions, ind/m2
    ## aphids present only on two central boxes
    APHIDS        <- rep(0, times = numboxes)
    APHIDS[30:31] <- 1
    state         <- c(APHIDS = APHIDS)      # initialise state variables

    ## RUNNING the model:
    times <- seq(0, 200, by = 1)   # output wanted at these time intervals
    out   <- ode.band(state, times, Aphid, parms = 0,
                      nspec = 1, names = "Aphid")

    ## ================
    ## Plotting output
    ## ================
    image(out, grid = Distance, method = "filled.contour",
          xlab = "time, days", ylab = "Distance on plant, m",
          main = "Aphid density on a row of plants")

    matplot.1D(out, grid = Distance, type = "l",
       subset = time %in% seq(0, 200, by = 10))

    # add an observed dataset to 1-D plot (make sure to use correct name):
    data <- cbind(dist  = c(0,10, 20,  30,  40, 50, 60),
                  Aphid = c(0,0.1,0.25,0.5,0.25,0.1,0))

    matplot.1D(out, grid = Distance, type = "l",
       subset = time %in% seq(0, 200, by = 10),
       obs = data, obspar = list(pch = 18, cex = 2, col="red"))
    ## Not run:
    plot.1D(out, grid = Distance, type = "l")

    ## End(Not run)

[Package deSolve version 1.24 Index]