# Solve Delay Differential Equations

### Description

A solver for systems of delay differential equations based on
numerical routines from Simon Wood's *solv95* program. This
solver is also capable of solving systems of ordinary differential
equations.

Please see the included demos for examples of how to use `dde`

.

To view available demos run `demo(package="PBSddesolve")`

.

The supplied demos require that the R package PBSmodelling
be installed.

### Usage

1 2 |

### Arguments

`y` |
Vector of initial values of the DDE system. The size of the supplied vector determines the number of variables in the system. |

`times` |
Numeric vector of specific times to solve. |

`func` |
A user supplied function that computes the gradients in
the DDE system at time The argument |

`parms` |
Any constant parameters to pass to |

`switchfunc` |
An optional function that is used to manipulate
state values at given times. The switch function takes the
arguments |

`mapfunc` |
If |

`tol` |
Maximum error tolerated at each time step (as a proportion of the state variable concerned). |

`dt` |
Maximum initial time step. |

`hbsize` |
History buffer size required for solving DDEs. |

### Details

The user supplied function `func`

can access past values (lags)
of `y`

by calling the `pastvalue`

function. Past gradients are accessible by the
`pastgradient`

function. These functions
can only be called from `func`

and can only be passed values
of `t`

greater or equal to the start time, but less than the
current time of the integration point. For example, calling
`pastvalue(t)`

is not allowed, since these values are the
current values which are passed in as `y`

.

### Value

A data frame with one column for `t`

, a column for every
variable in the system, and a column for every additional value that
may (or may not) have been returned by `func`

in the second
element of the list.

If the initial `y`

values parameter was named, then the solved
values column will use the same names. Otherwise `y1`

,
`y2`

, ... will be used.

If `func`

returned a list, with a named vector as the second
element, then those names will be used as the column names. If the
vector was not named, then `extra1`

, `extra2`

, ... will be
used.

### See Also

`pastvalue`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | ```
##################################################
# This is just a single example of using dde.
# For more examples see demo(package="PBSddesolve")
# the demos require the package PBSmodelling
##################################################
require(PBSddesolve)
local(env=.PBSddeEnv, expr={
#create a func to return dde gradient
yprime <- function(t,y,parms) {
if (t < parms$tau)
lag <- parms$initial
else
lag <- pastvalue(t - parms$tau)
y1 <- parms$a * y[1] - (y[1]^3/3) + parms$m * (lag[1] - y[1])
y2 <- y[1] - y[2]
return(c(y1,y2))
}
#define initial values and parameters
yinit <- c(1,1)
parms <- list(tau=3, a=2, m=-10, initial=yinit)
# solve the dde system
yout <- dde(y=yinit,times=seq(0,30,0.1),func=yprime,parms=parms)
# and display the results
plot(yout$time, yout$y1, type="l", col="red", xlab="t", ylab="y",
ylim=c(min(yout$y1, yout$y2), max(yout$y1, yout$y2)))
lines(yout$time, yout$y2, col="blue")
legend("topleft", legend = c("y1", "y2"),lwd=2, lty = 1,
xjust = 1, yjust = 1, col = c("red","blue"))
})
``` |

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