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DEtools

  

dfieldplot

  

plot direction field to a system of DEs

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

dfieldplot(deqns, vars, trange, xrange, yrange, options)

Parameters

deqns

-

list or set of first order ordinary differential equations

vars

-

list or set of dependent variables

trange

-

range of the independent variable

xrange

-

range of the first dependent variable

yrange

-

range of the second dependent variable

options

-

(optional) equations of the form keyword=value

Description

• 

Given either a system of two first order autonomous differential equations, or a single first order differential equation, dfieldplot produces a direction field plot. There can be only one independent variable.

• 

For plotting solution curves, see DEplot or phaseportrait.

• 

The direction field presented consists of a grid of arrows tangential to solution curves. For each grid point, the arrow centered at (x,y) will have slope dydx. For system of two first order autonomous differential equations this slope is computed using dydt/dxdt, where these two derivatives are specified in the first argument to dfieldplot. Note: A system is determined to be autonomous when all terms and factors, other than the differential, are free of the independent variable. For more information, see DEtools[autonomous]. For the single first order differential equation, the slope is simply dydx.

• 

Optional equations for dfieldplot are in the DEplot help page.

• 

The xrange and yrange parameters must be specified as follows.

xt=x1..x2,  yt=y1..y2  or

   x=x1..x2,     y=y1..y2

  

By default, integration along a solution curve stops one mesh point after the specified range is exceeded.  This may be overridden by the obsrange option.

Examples

To execute this section, open this help page as a worksheet and then execute the worksheet.

withDEtools:

Example of a single non-autonomous first order differential equation:

dfieldplotⅆⅆxyx=1xx2+4yx122,yx,x=3..3,y=3..2,title=`Restricted domain`,color=1xx2+4y2

Example of a system of two autonomous first order differential equations. This is the command to create the plot from the Plotting Guide.

dfieldplotⅆⅆtxt=xt1yt,ⅆⅆtyt=0.3ytxt1,xt,yt,t=2..2,x=1..2,y=1..2,arrows=SLIM,color=black,dirfield=10,10

See Also

DEplot

DEtools

DEtools[autonomous]

DEtools[phaseportrait]

dsolve[classical]

dsolve[dverk78]

dsolve[gear]

dsolve[lsode]

dsolve[numeric]

dsolve[rkf45]

plot

plots[odeplot]

 


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