Application Guide

7. To enter additional ODEs, press the down arrow to display the next ODE edit field.
As you move among defined ODEs, the graph is updated to reflect any changes.
One solution to the ODE is graphed for each IC specified for each shown ODE
(selected by check box).
Summary of Differential Equation Settings
Solution
Method
Selects Euler or Runge-Kutta as the numerical solution method.
Iterations
Between
Plot Step
Computational accuracy for Euler solution method only. Must be an
integer value>0. To restore the default, select the down-arrow and
select Default.
Error
Tolerance
Computational accuracy for Runge-Kutta solution method only. Must be a
floating-point value|1×10
-14
. To restore the default, select the down-
arrow and select Default.
Field
None - No field is plotted. Available for any number of ODEs, but
required if three or more 1st-order ODEs are active. Graphs a
combination of the solution and/or values of one or more ODEs
(according to user-configured Axes settings).
Slope - Plots a field representing the family of solutions to a single 1st-
order ODE. Exactly one ODE must be active. Sets Axes to Default
(xandy). Sets Horizontal axis to x (the independent variable). Sets
Vertical axis to y (the solution to the ODE).
Direction - Graphs a field in the phase plane representing the relationship
between a solution and/or values of a system of two 1st-order ODEs (as
specified by the CustomAxes setting). Exactly two ODEs must be active.
Axes
Default (x and y) - Plots x on the x axis and y (the solutions to the active
differential equations) on the y axis.
Custom - Lets you select the values to be plotted on the x and y axes
respectively. Valid entries include:
• x (the independent variable)
• y1, y2, and any identifiers defined in the ODE editor
• y1’, y2’, and any derivatives defined in the ODE editor
Plot Start
Sets the independent variable value at which the solution plot starts.
Plot End
Sets the independent variable value at which the solution plot stops.
Plot Step
Sets the increment of the independent variable at which values are
plotted.
Field
Resolution
Sets the number of columns of field rendering elements (line segments)
used to draw a slope or direction field. You can change this parameter
only if Field = Direction or Slope.
Direction
Field at x=
Sets the independent variable value at which a direction field is drawn
when plotting non-autonomous equations (those that refer to x). Ignored
Graphs Application 189