# ex_vdpol: van der Pol Equation, Nonlinear Vacuum Tube Circuit, ODE In deTestSet: Test Set for Differential Equations

## Description

Problem originating from electronics, describing the behavior of nonlinear vacuum tube circuots.

It is an ODE, 2 equations.

## Usage

 ```1 2 3``` ```vdpol (times = 0:2000, yini = NULL, parms = list(), printmescd = TRUE, atol = 1e-6, rtol = 1e-6, ...) ```

## Arguments

 `yini ` the initial (state) values for the DE system. 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. `parms ` list of parameters that overrule the default parameter values `atol ` absolute error tolerance, either a scalar or a vector, one value for each y. `rtol ` relative error tolerance, either a scalar or a vector, one value for each y, `printmescd ` if TRUE the mixed error significant digits computed using the reference solution at time 5 are printed `... ` additional arguments passed to the solver .

## Details

The default parameters are: mu=1000

The default initial conditions are: y1 = 2, y2 = 0

## Value

A matrix of class `deSolve` with up to as many rows as elements in `times` and as many columns as elements in `yini`, plus an additional column (the first) for the time value.

There will be one row for each element in `times` unless the solver returns with an unrecoverable error. If `yini` has a names attribute, it will be used to label the columns of the output value.

## Note

This model is implemented in R

## Author(s)

Karline Soetaert <[email protected]>

Francesca Mazzia <[email protected]>

## Examples

 ```1 2 3 4 5``` ```out <- vdpol() plot(out, lwd = 2, which = 1) # compare to reference solution out[nrow(out),-1] - reference("vdpol") ```

deTestSet documentation built on May 29, 2017, 2:56 p.m.