DiffEqs`DEGraphics`

This package provides the following functions for plotting solutions of differential equations.

DEPlot[f[t, y], {t, tmin, tmax}, {y, ymin, ymax}] creates a plot showing the direction field and solution curves for the differential equation y' = f[t, y].

PhasePlot[{f[x, y], g[x, y]}, {t, tmin, tmax}, {x, xmin, xmax}, {y, ymin, ymax}]  creates a plot showing the direction field and solution curves for the autonomous system  x' = f[x, y], y' = g[x, y].

PhasePlot[{f[t, x, y], g[t, x, y]}, {t, tmin, tmax}, {x, xmin, xmax}, {y, ymin, ymax}]   creates a plot showing solution curves for the system  x' = f[t, x, y], y' = g[t, x, y].

NDPlot[eqns, fns, {t, tmin, tmax}uses NDSolve to compute a numerical solution of a system of (up to 3) first-order differential equations and plots the solution. Returns {solution, -Graphics-}.

PoincareTimeSection[{f[t, x, y], g[t, x, y]}, {t, t0, tmax, dt}, {x, x0 }, {y, y0 }] creates a Poincaré time section plot of the solution of   x' = f[t, x, y], x[t0] = x0, y' = g[t, x, y], y[t0] = y0.

ViewProjections[{f[t], g[t], h[t]}, {t, t0, tmax}, {x, y, z}] creates a GraphicsArray of projections of the curve (f[t], g[t], h[t]) onto the xy, xz, and yz coordinate planes.

PlotImplicit[F[t, y], {t, tmin, tmax}, {y, ymin, ymax}] creates a contour plot of the function F.

TimeStatePlot[{x[t], y[t]}, {t, tmin, tmax}, {y, ymin, ymax}] creates a 3D plot of the ``time-state trajectory" (t, x[t], y[t]) with projections onto the t x, t y, and x y planes.

     
Plotting solutions of differential equations.

 

This loads the package.

<<DiffEqs`DEGraphics`

 

DEPlot

PhasePlot

NDPlot

PoincareTimeSection

Here is an example of the use of PoincareTimeSection.

[Graphics:Images/index_gr_73.gif]

[Graphics:Images/index_gr_74.gif]



Options for PoincareTimeSection are the same as for ListPlot.

 


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ViewProjections

Here is an example of the use of ViewProjections.

[Graphics:Images/index_gr_76.gif]

[Graphics:Images/index_gr_77.gif]



Options for ViewProjections are the same as for ParametricPlot and GraphicsArray with the addition of:

[Graphics:Images/index_gr_79.gif]
        Options for ViewProjections.

 


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TimeStatePlot

An example of the use of TimeStatePlot:

[Graphics:Images/index_gr_80.gif]

[Graphics:Images/index_gr_81.gif]

To plot the solution of a pair of differential equations, one must provide TimeStatePlot with the solution.

[Graphics:Images/index_gr_82.gif]

[Graphics:Images/index_gr_83.gif]

TimeStatePlot uses ParametricPlot3D and Shadow from the Graphics3D package. The options of ParametricPlot3D can be used, as well as the following:

[Graphics:Images/index_gr_84.gif]
        Options for TimeStatePlot.

Here's an example in which several options are used.

[Graphics:Images/index_gr_85.gif]

[Graphics:Images/index_gr_86.gif]

If you specify PlotRange (e.g., when making an animation) , you'll need to make adjustments to the ShadowPositions.

[Graphics:Images/index_gr_87.gif]

[Graphics:Images/index_gr_88.gif]


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PlotImplicit

Examples of the use of PlotImplicit:

[Graphics:Images/index_gr_89.gif]

[Graphics:Images/index_gr_90.gif]

[Graphics:Images/index_gr_91.gif]

[Graphics:Images/index_gr_92.gif]

PlotImplicit uses ContourPlot and DensityPlot and accepts any of their options. In addition, the following option can be used.

[Graphics:Images/index_gr_93.gif]
        Options for PlotImplicit.

 

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Converted by Mathematica      June 9, 2002