Equation Trekker Package Symbol

EquationTrekker

EquationTrekker[eqn, x, {t, t_min, t_max}]
opens a graphical interface for specifying initial conditions and plotting the resulting numerical solution to the first or second order ordinary differential equation eqn for the function x with the independent variable t in the range t_min to t_max.

EquationTrekker[eqns, {x, y}, {t, t_min, t_max}]
opens a graphical interface for specifying initial conditions and plotting the resulting numerical solution to the system of two first order ordinary differential equations eqns for the functions x and y.

EquationTrekker[state]
reopens a graphical interface with the treks saved in the EquationTrekkerState object state.

MORE INFORMATION

To use EquationTrekker, you first need to load the Equation Trekker Package using Needs["EquationTrekker`"].

If eqn is a single first order ODE, plots of x[t] versus t are displayed. If eqn is a single second order ODE, plots of x'[t] versus x[t] are displayed. If eqns consist of a system of two first order ODEs, plots of y[t] versus x[t] are displayed.

Treks are invoked by right-clicking a coordinate, which generates a trek that starts at the point specified by the mouse cursor.

The initial position of a trek is highlighted in yellow, and by default corresponds to an initial condition specified at t=0. However, only the section of the trek from t_min to t_max is displayed, with the coordinate associated with t_min displayed as a point and the coordinate associated with t_max displayed as an arrowhead.

Changing defaults for newly created treks may be accomplished by typing a value in the text field and clicking the button.

EquationTrekker generates a modal dialog, and the kernel is controlled by the graphical interface until the window is closed.

When the window is closed, a list containing an EquationTrekkerState object and a graphic is returned. The EquationTrekkerState object contains all of the information necessary to reopen the window with the treks that were displayed when the window was closed.

The following options can be given:

ImageSize	{400,400}	absolute size of EquationTrekker window
PlotRange	{Automatic,{-1,1}}	range of values to include
TrekParameters	{}	list of parameters and parameter ranges
TrekGenerator	DifferentialEquationTrek	method used to generate treks

A valid setting for TrekParameters is a list of rules of the form param->range, where range consists of a starting value and a range, {v, {v_min, v_max}}. The range specification may also consist of a single value v, which is equivalent to {v, {0, 2v}}.

Valid settings for TrekGenerator are DifferentialEquationTrek and PoincareSection.

The default setting TrekGenerator->DifferentialEquationTrek creates treks by following the path of the dependent variables generated using NDSolve.

The setting TrekGenerator->PoincareSection creates treks by sampling the phase space. The sampling interval is typically periodic.

The setting TrekGenerator->{method, subopts} may be used to include the suboptions subopts for the TrekGenerator method method.

EXAMPLES

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Basic Examples (1)

Needs["EquationTrekker`"]

This is a simple example demonstrating how EquationTrekker operates:

In[2]:=

A window similar to the one below will appear (but with an empty canvas). Click the canvas to add treks:

Options (1)