[ < ] [ > ]   [ << ] [ Up ] [ >> ]         [Top] [Contents] [Index] [ ? ]

63. plotdf


[ < ] [ > ]   [ << ] [ Up ] [ >> ]         [Top] [Contents] [Index] [ ? ]

63.1 Introduction to plotdf

The function plotdf creates a plot of the direction field of a first-order Ordinary Differential Equation (ODE) or a system of two autonomous first-order ODE's.

To plot the direction field of a single ODE, the ODE must be written in the form:

 
       dy
       -- = F(x,y)
       dx

and the function F should be given as the argument for plotdf. The independent variable is always identified as x, and the dependent variable as y. Those two variables should not have any values assigned to them.

To plot the direction field of a set of two autonomous ODE's, they must be written in the form

 
       dx             dy
       -- = G(x,y)    -- = F(x,y) 
       dt             dt

and the argument for plotdf should be a list with the two functions F and G, in any order.

If only one ODE is given, plotdf will implicitly admit x=t, and G(x,y)=1, transforming the non-autonomous equation into a system of two autonomous equations.


[ < ] [ > ]   [ << ] [ Up ] [ >> ]         [Top] [Contents] [Index] [ ? ]

63.2 Definitions for plotdf

Function: plotdf (dydx,...options...)
Function: plotdf ([dxdt,dydt],...options...)

Displays a direction field in two dimensions x and y.

dydx, dxdt and dydt are expressions that depend on x and y. In addition to those two variables, the expressions can also depend on a set of parameters, with numerical values given with the parameters option (the option syntax is given below), or with an range of allowed values specified by a sliders option.

Several other options can be given within the command, or entered into the menu that will appear when the upper-left corner of the plot window is clicked. Integral curves can be obtained by clicking on the plot, or with the option trajectory_at. The direction of the integration can be controlled with the direction option, which can have values of "forward", "backward" or "both". The number of integration steps is given by nsteps and the time interval between them is set up with the tstep option. The Adams Moulton method is used for the integration; it is also possible to switch to an adaptive Runge-Kutta 4th order method.

Plot window menu:

The menu in the plot window has the following options: "Zoom", will change the behavior of the mouse so that it will allow you to zoom in on a region of the plot by clicking with the left button. Each click near a point magnifies the plot, keeping the center at the point where you clicked. Holding the SHIFT key while clicking, zooms out to the previous magnification. To resume computing trajectories when you click on a point, select "Integrate" from the menu.

The option "Config" in the menu can be used to change the ODE(s) in use and various other settings. After configuration changes are made, the menu option "Replot" should be selected, to activate the new settings. If a pair of coordinates are entered in the field "Trajectory at" in the "Config" dialog menu, and the "enter" key is pressed, a new integral curve will be shown, in addition to the ones already shown. When "Replot" is selected, only the last integral curve entered will be shown.

Holding the right mouse button down while the cursor is moved, can be used to drag the plot sideways or up and down. Additional parameters such as the number of steps, the initial value of t and the x and y centers and radii, may be set in the Config menu.

A copy of the plot can be printed to a Postscript printer, or saved as a postscript file, using the menu option "Save". To switch between printing and saving to a Postscript file, "Print Options" should be selected in the dialog window of "Config". After the settings in the "Save" dialog window are entered, "Save" must be selected in the first menu, to create the file or print the plot.

Plot options:

The plotdf command may include several commands, each command is a list of two or more items. The first item is the name of the option, and the remainder comprises the value or values assigned to the option.

The options which are recognized by plotdf are the following:

Examples:

NOTE: Due to a bug in openmath, all commands that use it, in particular plotdf, must end with a semicolon and not with a dollar sign. The dollar sign might work in some of the graphical interfaces to Maxima, but to avoid problems we will use a semicolon in all the examples below.

To use this function write first load("plotdf").


[ << ] [ >> ]           [Top] [Contents] [Index] [ ? ]

This document was generated by Robert Dodier on September, 20 2006 using texi2html 1.76.