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.

Options for PoincareTimeSection are the same as for ListPlot.

ViewProjections

Here is an example of the use of ViewProjections.

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

        Options for ViewProjections.

TimeStatePlot

An example of the use of TimeStatePlot:

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

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

        Options for TimeStatePlot.

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

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

PlotImplicit

Examples of the use of PlotImplicit:

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

        Options for PlotImplicit.

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