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

Here is an example of the use of PhasePlot, with the default value of InitialPoints. The system is [Graphics:Images/index_gr_50.gif].

[Graphics:Images/index_gr_51.gif]

[Graphics:Images/index_gr_52.gif]



No direction field is drawn if the vector field depends on t.

[Graphics:Images/index_gr_54.gif]

[Graphics:Images/index_gr_55.gif]



This uses the Fitzhugh-Nagumo equations and a single initial point.

[Graphics:Images/index_gr_57.gif]

[Graphics:Images/index_gr_58.gif]



Options for PhasePlot are the same as for DEPlot, except that Isoclines is replaced by ShowNullclines.

[Graphics:Images/index_gr_60.gif]
        Options for PhasePlot.

One more nice example:

[Graphics:Images/index_gr_61.gif]

[Graphics:Images/index_gr_62.gif]




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NDPlot

Here are three examples of the use of NDPlot.

[Graphics:Images/index_gr_64.gif]

[Graphics:Images/index_gr_65.gif]

[Graphics:Images/index_gr_66.gif]


[Graphics:Images/index_gr_67.gif]

[Graphics:Images/index_gr_68.gif]

[Graphics:Images/index_gr_69.gif]


[Graphics:Images/index_gr_70.gif]

[Graphics:Images/index_gr_71.gif]

[Graphics:Images/index_gr_72.gif]

Any of the options for NDSolve, Plot, ParametricPlot, or ParametricPlot3D can be used in NDPlot.

 


PoincareTimeSection

ViewProjections

TimeStatePlot

PlotImplicit

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Converted by Mathematica      June 9, 2002